Answer: The pH of 0.10 M [tex]Cu(NO_{3})_{2}(aq)[/tex] is 4.49.
Explanation:
Given: Initial concentration of [tex]Cu(H_{2}O)^{2+}_{6}[/tex] = 0.10 M
[tex]K_{a} = 1.0 \times 10^{-8}[/tex]
Let us assume that amount of [tex]Cu(H_{2}O)^{2+}_{6}[/tex] dissociates is x. So, ICE table for dissociation of [tex]Cu(H_{2}O)^{2+}_{6}[/tex] is as follows.
[tex]Cu(H_{2}O)^{2+}_{6} \rightleftharpoons [Cu(H_{2}O)_{5}(OH)]^{+} + H_{3}O^{+}[/tex]
Initial: 0.10 M 0 0
Change: -x +x +x
Equilibrium: (0.10 - x) M x x
As the value of [tex]K_{a}[/tex] is very small. So, it is assumed that the compound will dissociate very less. Hence, x << 0.10 M.
And, (0.10 - x) will be approximately equal to 0.10 M.
The expression for [tex]K_{a}[/tex] value is as follows.
[tex]K_{a} = \frac{[Cu(H_{2}O)^{2+}_{6}][H_{3}O^{+}]}{[Cu(H_{2}O)^{2+}_{6}]}\\1.0 \times 10^{-8} = \frac{x \times x}{0.10}\\x = 3.2 \times 10^{-5}[/tex]
Hence, [tex][H_{3}O^{+}] = 3.2 \times 10^{-5}[/tex]
Formula to calculate pH is as follows.
[tex]pH = -log [H^{+}][/tex]
Substitute the values into above formula as follows.
[tex]pH = -log [H^{+}]\\= - log (3.2 \times 10^{-5})\\= 4.49[/tex]
Thus, we can conclude that the pH of 0.10 M [tex]Cu(NO_{3})_{2}(aq)[/tex] is 4.49.
What is the major product in this reaction
Answer:
I think option A is right answer
In the given range,at what temperature does oxy gen have the highest solubility?
According to the kinetic theory, all matter is made of moving particles, which measurement of matter is directly proportional to the
average kinetic energy of the particles?
Calculate the molarity of a 17.5% (by mass) aqueous solution of nitric acid. Select one: a. 2.74 m b. 4.33 m c. 0.274 m d. 3.04 m e. The density of the solution is needed to solve the problem.
Answer:
Option e.
Explanation:
Molarity is the concentration that indicates moles of solute in 1 L of solution.
We have another concentration, percent by mass.
Percent by mass indicates mass of solute in 100 g of solution.
Our solute is HNO₃, our solvent is water.
17.5 g of nitric acid is the mass of solute. We can convert them to moles:
17.5 g . 1mol / 63g = 0.278 moles
We do not have volume of solution. We assume the mass is 100 g because the percent by mass but we need density to state the volume.
Density = Mass / Volume
Mass / Density = Volume
Once we have the volume, we need to be sure the units is in L, to determine molarity
M = mol /L
once formed, how are coordinate covalent bonds different from other covalent bonds?
Answer:
[tex]\boxed {\boxed {\sf {One \ atom \ donates \ both \ electrons \ in \ a \ pair}}}[/tex]
Explanation:
A covalent bond involves the sharing of electrons to make the atoms more stable, and so they satisfy the Octet Rule (8 valence electrons).
Typically each atom contributes an electron to form an electron pair. This is a single bond. There are also double bonds (two pairs of electrons), triple bonds (three pairs of electrons), and coordinate covalent bonds.
Sometimes, to satisfy the Octet Rule and achieve stability, one atom contributes both of the electrons in an electron pair. This is different from other covalent bonds because usually each of the 2 atoms contributes an electron to make a pair.
How many electrons are shown in the following electron
configuration: 1s22s22p63s 23p64s23d104p65s24d105p66s2 ?
Express your answer numerically as an integer.
Answer:
1s22s22p6
Explanation:
Neon is an element in the periodic table and has an atomic number of 10, which means it has 10 protons in its nucleus and thus since the number of protons and electrons is the same then it has 10 electrons.
Therefore, it has 2 electrons in the first energy shell and 8 electrons in the second energy shell. To elaborate further, the first shell has a single s-sub shell that contains a single s-orbital that can hold two electrons. The second energy shell has a single s-sub-shell whose s-orbital will occupy 2 electrons, and also has a p-orbital which can hold 6 electrons, making the second shell to have 8 electrons.
dentify the correct formula for the following ionic compounds. - sodium chloride - magnesium chloride - calcium oxide - lithium phosphide - aluminum sulfide - calcium nitride A. SCl B. LiP 3 C. AlS D. Li 3P E. CaN F. CaO G. Ca 3N 2 H. MgCl 2 I. NaCl J. CaO 2 K. CaN 2 L. LiP M. MnCl 2 N. Al 2S 3 O. AlS 3
Explanation:
The chemical formula of an ionic compound can be written by using the symbols of the respective cations and anions.
The overall charge on the molecule should be zero.
Hence, the total charge of cations=total charge of anions.
The symbols of the given molecules are shown below:
sodium chloride ---- NaCl
magnesium chloride ---[tex]MgCl_2[/tex]
calcium oxide ---- CaO
lithium phosphide----[tex]Li_3P[/tex]
aluminum sulfide ----- [tex]Al_2S_3[/tex]
calcium nitride---- [tex]Ca_3N_2[/tex]
cual es la masa atomica del hidrogeno
El hidrógeno es el elemento químico de número atómico 1, representado por el símbolo H. Con una masa atómica de 1.00784 u es el más ligero de la tabla periódica de los elementos. Por lo general, se presenta en su forma molecular, formando el gas diatómico H₂ en condiciones normales.
A sample of oxygen gas has a volume of 89.6 L at STP. How many moles of oxygen gas are present ?
Answer:
89,6/22,4 =4(mol)
Explanation:
There are approximately 1.089 moles of oxygen gas present in the sample at STP.
At STP (Standard Temperature and Pressure), the conditions are defined as follows:
Temperature (T) = 0 degrees Celsius = 273.15 Kelvin
Pressure (P) = 1 atmosphere (atm) = 101.325 kPa = 1013.25 hPa
Now, to find the number of moles of oxygen gas (O2) present in the sample, we can use the ideal gas law:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant = 0.0821 L.atm/(mol.K)
T = temperature (in Kelvin)
Given:
V = 89.6 L (volume at STP)
T = 273.15 K (STP temperature)
Let's plug in the values and solve for n (number of moles):
n = PV / RT
n = (1 atm) × (89.6 L) / (0.0821 L.atm/(mol.K) × 273.15 K)
n = 1.089 moles
So, there are approximately 1.089 moles of oxygen gas present in the sample at STP.
To know more about oxygen gas:
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explain in brief how some bacteria cause tooth cavities
Answer:
because some bacteria change the ph of the teeth and leads to tooth cavitiew
Poly(ethylene terephthalate) (PET), which has glass transition (Tg) and crystalline melting (Tm) temperature of 69 and 267 °C, respectively, can exist in a number of different states depending upon temperature and thermal history. Thus, it is possible to prepare materials that are semicrystalline with amorphous regions that are either glassy or rubbery and amorphous materials that are glassy, rubbery or melts. Consider a sample of PET cooled rapidly from 300 °C (state A) to room temperature. The resulting material is rigid and perfectly transparent (state B). The sample is then heated to 100 °C and maintained at this temperature, during which time is gradually becomes translucent (state C). It is then cooled to room temperature, where it is again observed to be translucent (state D).
Answer:
Following are the solution to the given points:
Explanation:
For point A:
The sample cooking (PET) is between 300°C and room temperature.Now in nature, the substance is exceedingly stiff.Samples of PET up to 100°C were heated and stayed on equal footing.Now it has cooled off the same sample below 100° C and we may see how it is again TRASNEPARENT in nature.For point B:
In point 3, the mixture was added to 100°C, which implies that the granular material flows and deforms, enabling it to become elongated. This is termed solid-state crystalline such that grains are flexible, but this material contaminates numerous little crystalline that has spheres when we cool down in point 4 polymers. It forms therefore an unstructured solid, which then in point 4 is higher in particles and less pliable in orderly atoms.
For point C:
In point 2, the specimen gets forced at room temperature to organize a huge molecule in an ordinary and crystal fashion and therefore is transparent due to highly crystalline atoms in point 2 of the PET sample.
In point 4, however, we notice how amorphous, firm but not crystalline develops. It's why light tends to disperse over many cereal limits, since many microscopic crystallines, therefore dispersion, PET in point 4 is translucent.
A rectangular piece of plastic has a width of 4.2 cm, a height of 1.9 cm and a length of 8.8 cm. If the mass of the plastic rectangle is 64.6 g, what is its density in g/mL?
Answer:
0.92g/mL
Explanation:
Density of a substance is calculated as follows:
Density = mass (m) ÷ volume (V)
According to this question, a rectangular piece of plastic has a width of 4.2 cm, a height of 1.9 cm and a length of 8.8 cm. Using the formula; L × W × H, the volume of the plastic can be calculated
V = L × W × H
V = 8.8 × 4.2 × 1.9
V = 70.2cm³
The mass of the plastic is 64.6g, hence, its density is:
Density = 64.6g ÷ 70.2cm³
Density of the rectangular plastic = 0.92g/cm³ or 0.92g/mL
Help!!!!!!!!!
I'm using plato
Answer:
- Two black balls: they represent a diatomic molecule composed by two atoms of the same element.
- One black ball and two black balls: they represent a compound formed by two different elements.
- One gray ball and two black balls: they represent a compound formed by two different elements.
- Two black-dotted balls: they represent a diatomic molecule composed by two atoms of the same element.
Explanation:
Hey there!
In this case, according to the given information, we can firstly bear to mind the fact that each ball color represents a different element, for that reason we can tell the following:
- Two black balls: they represent a diatomic molecule composed by two atoms of the same element.
- One black ball and two black balls: they represent a compound formed by two different elements.
- One gray ball and two black balls: they represent a compound formed by two different elements.
- Two black-dotted balls: they represent a diatomic molecule composed by two atoms of the same element.
Regards!
Determine whether the reaction will be spontaneous at high temperatures only, at low temperatures only, at all temperatures, or no temperatures. (HINT: Use your chemical sense and your real-world knowledge to predict the signs of delta Hrxn & delta Srxn)
4Fe(s) + 3O2(g) ----> 2Fe2O3(s) [rust]
Circle one:High T, Low T, All T, No T
Answer:
The rusting of iron is spontaneous at low temperatures.
Explanation:
The given chemical reaction is:
4Fe(s) + 3O2(g) ----> 2Fe2O3(s) [rust]
The rusting of iron is a chemical reaction in which iron reacts with oxygen in presence of moisture and forms iron oxide.
This reaction takes place in a faster rate when there is low temperatures in the atmosphere.
When temperature is low, the moisture in the atmosphere is more and hence, rate of rusting is more.
Identify the highest energy molecular process that occurs when a molecule absorbs a microwave photon.
The question is incomplete, the complete question is;
Identify the highest energy molecular process that occurs when a molecule absorbs a microwave photon
a) electronic excitation
b) bond breakage
c) molecular vibration
d) molecular rotation
Answer:
molecular rotation
Explanation:
Microwaves are part of the electromagnetic spectrum. They are lower energy, lower frequency radiation.
When molecules absorb infrared radiation, they transition between the rotational states of the molecule.
Hence, the highest energy molecular process that occurs when a molecule absorbs a microwave photon is molecular rotation.
The reversible reaction: 2SO2(g) O2(g) darrow-tn.gif 2SO3(g) has come to equilibrium in a vessel of specific volume at a given temperature. Before the reaction began, the concentrations of the reactants were 0.060 mol/L of SO2 and 0.050 mol/L of O2. After equilibrium is reached, the concentration of SO3 is 0.040 mol/L. What is the equilibrium concentration of O2
Answer:
[tex][O_2]_{eq}=0.030M[/tex]
Explanation:
Hello there!
In this case, according to the given information, it turns out possible for us to solve this problem by firstly writing out the mathematical expression for the concentration of oxygen at equilibrium, given the initial one and the change due to the reaction extent:
[tex][O_2]_{eq}=0.050M-x[/tex]
Whereas [tex]x[/tex] can be found considering the equilibrium of SO3:
[tex][SO_3]_{eq}=2x=0.040M[/tex]
Which means:
[tex]x=\frac{0.040M}{2} =0.020M[/tex]
Thus, the equilibrium concentration of oxygen gas turns out:
[tex][O_2]_{eq}=0.050M-0.020M=0.030M[/tex]
Regards!
A student prepares a aqueous solution of acetic acid . Calculate the fraction of acetic acid that is in the dissociated form in his solution. Express your answer as a percentage. You will probably find some useful data in the ALEKS Data resource.
Answer:
10.71%
Explanation:
The dissociation of acetic acid can be well expressed as follow:
CH₃COOH ⇄ CH₃COO⁻ + H⁺
Let assume that the prepared amount of the aqueous solution is 14mM since it is not given:
Then:
The I.C.E Table is expressed as follows:
CH₃COOH ⇄ CH₃COO⁻ + H⁺
Initial 0.0014 0 0
Change - x +x +x
Equilibrium (0.0014 - x) x x
Recall that:
Ka for acetic acid CH₃COOH = 1.8×10⁻⁵
∴
[tex]K_a = \dfrac{[x][x]]}{[0.0014-x]}[/tex]
[tex]1.8*10^{-5} = \dfrac{[x][x]]}{[0.0014-x]}[/tex]
[tex]1.8*10^{-5} = \dfrac{[x]^2}{[0.0014-x]}[/tex]
[tex]1.8*10^{-5}(0.0014-x) = x^2[/tex]
[tex]2.52*10^{-8} -1.8*10^{-5}x = x^2[/tex]
[tex]2.52*10^{-8} -1.8*10^{-5}x - x^2 =0[/tex]
By rearrangement:
[tex]- x^2 -1.8*10^{-5}x +2.52*10^{-8}= 0[/tex]
Multiplying through by (-) and solving the quadratic equation:
[tex]x^2 +1.8*10^{-5}x-2.52*10^{-8}= 0[/tex]
[tex](-0.00015 + x) (0.000168 + x) =0[/tex]
x = 0.00015 or x = -0.000168
We will only consider the positive value;
so x=[CH₃COO⁻] = [H⁺] = 0.00015
CH₃COOH = (0.0014 - 0.00015) = 0.00125
However, the percentage fraction of the dissociated acetic acid is:
[tex]= \dfrac{ 0.00015}{0.0014}\times 100[/tex]
= 10.71%
Identify the oxidation half-reaction for this reaction:
Fe(s) + 2HCl(aq) → FeCl2(aq) + H2(g)
A. Fe2+ + 2e → Fe(s)
O B. H2(g) → 2H+ + 2e
O C. Fe(s) → Fe2+ + 2e
O D. 2H+ + 2e → H2(9)
Answer:
Fe(s)->Fe2+2e-
Explanation:
A.p.e.x
The oxidation half-reaction for the given reaction is Fe(s) → Fe²⁺ + 2e⁻ Hence, Option (C) is correct
What is Oxidation reaction ?Oxidation reaction is a chemical reaction which can be described as follows ;
Addition of oxygen Removal of hydrogen Loss of ElectronAddition of electronegative atomRemoval of Electropositive elementIn the given reaction ;
Fe(s) + 2HCl(aq) → FeCl₂(aq) + H₂(g)
Fe at RHS got converted to Fe²⁺ state at LHS which shows the gain of electron by Fe with in the reaction.
Therefore,
The oxidation half-reaction for the given reaction is Fe(s) → Fe²⁺ + 2e⁻ Hence, Option (C) is correct
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Classify each molecule as an alcohol, ketone, or aldehyde based on its name. Propanone (acetone) Choose... Ethanal Choose... 3-phenyl-2-propenal Choose... Butanone Choose... Ethanol Choose... 2-propanol Choose...
Answer:
1.) Propanone (ketone)
2.) Ethanal( aldehyde)
3.) 3-phenyl-2-propenal (aldehyde)
4.) Butanone (ketone)
5.) Ethanol ( alcohol)
6.) 2-propanol (alcohol)
Explanation:
In organic chemistry, ALCOHOL ( also known as alkanol) are compounds in which hydroxyl groups are linked to alkyl groups. They can be considered as being derived from the corresponding alkanes by replacing the hydrogen atoms with hydroxyl groups. The hydroxyl group is the functional group of the alcohol as it is responsible for their characteristic chemical properties. A typical example of alcohol is ethanol and 2-propanol.
Alkanals or ALDEHYDES have the general formula RCHO while alkanones or KETONES have the general formula RR'CO where R and R' may be alkyl or aryl groups. The main similarity between these two classes of compounds is the presence of the carbonyl group. In aldehydes, there is a hydrogen atom attached to the carbon In the carbonyl group while there is none on the ketones.
Some common examples of ketones are Propanone, Butanone while examples of aldehydes are Ethanal and 3-phenyl-2-propenal
complete the following steps.
Remember to follow lower numbered rules first.
Na2CO3(aq) + Pb(OH)2(aq) → NaOH (?) + PbCO3(?)
a. Write a balanced chemical equation. (1 pt)
b. If a reaction occurs, write the balanced
chemical equation with the proper states of matter
(i.e. solid, liquid, aqueous) filled in. If no reaction
occurs, write “No reaction.” (1 pt)
c. If a reaction occurs, write the net ionic equation
for the reaction. If no reaction occurs, write "no
reaction.” (1 pt)
Answer:
See explanation
Explanation:
a) The balanced reaction equation is;
Na2CO3(aq) + Pb(OH)2(aq) -----> 2 NaOH + PbCO3
b) When we include states of matter;
Na2CO3(aq) + Pb(OH)2(aq) -----> 2 NaOH(aq) + PbCO3 (s)
c) Complete ionic equation;
2Na^+(aq) + CO3^2-(aq) + Pb^2+(aq) + 2OH^-(aq) ----> 2Na^+(aq) + 2OH^-(aq) + PbCO3(s)
Net Ionic equation;
Pb^2+(aq) + CO3^2-(aq) ----> PbCO3(s)
A hypothetical A-B alloy of composition 53 wt% B-47 wt% A at some temperature is found to consist of mass fractions of 0.5 for both and phases. If the composition of the phase is 92 wt% B-8 wt% A, what is the composition of the phase
Answer:
the composition of the ∝ phase C∝ = 14 or [ 14 wt% B-86 wt% A ]
Explanation:
Given the data in the question;
Co = 53 or [ 53 wt% B-47 wt% A ]
W∝ = 0.5 = Wβ
Cβ = 92 or [ 92 wt% B-8 wt% A ]
Now, lets set up the Lever rule for W∝ as follows;
W∝ = [ Cβ - Co ] / [ Cβ - C∝ ]
so we substitute our given values into the expression;
0.5 = [ 92 - 53 ] / [ 92 - C∝ ]
0.5 = 39 / [ 92 - C∝ ]
0.5[ 92 - C∝ ] = 39
46 - 0.5C∝ = 39
0.5C∝ = 46 - 39
0.5C∝ = 7
C∝ = 7 / 0.5
C∝ = 14 or [ 14 wt% B-86 wt% A ]
Therefore, the composition of the ∝ phase C∝ = 14 or [ 14 wt% B-86 wt% A ]
Use the following key to classify each of the elements below in its elemental form:
A. Discrete atoms .. C. Metallic lattice
B. Molecules ... D. Extended, three-dimensional network
1. Magnesium
2. Nitrogen ...
3. Lithium
4. Potassium ...
Answer:
Magnesium - Metallic lattice
Nitrogen - Molecules
Lithium - Metallic lattice
Potassium - Metallic lattice
Explanation:
Metals exist in metallic lattices. In this lattice, metal ions are held together with a sea of electrons by strong electrostatic forces.
All metals possess this metallic lattice, hence; potassium, lithium and magnesium all consist of metal lattices.
Nitrogen is a nonmetal and consists of molecules of N2.
What is true about the properties of liquids and gases?
Gas particles are much more densely packed than liquid particles.
The crystal lattice structure of liquids is more defined than in gases.
Liquids form amorphous crystals while gases do not.
There are strong intermolecular forces between particles that make up liquids, but not gases.
Answer:
There are strong intermolecular forces between particles that make up liquids, but not gases.
Explanation:
Solids, liquids and gases are the three states of matter that exists. However, they possess varying properties that distinguishes them from one another. One of these properties is the strength of the intermolecular forces that hold their molecules together.
The intermolecular forces of each state of matter becomes weak in this order: solid>liquid>gas.
- Intermolecular forces in solid molecules are very strong, hence making them compact and well attached to each other.
- Intermolecular forces in liquid molecules are not too strong, hence, cannot exist in a fixed position but tend to flow.
- Intermolecular forces in gaseous molecules are very weak, hence, gases can move easily and rapidly in any given space.
5. A beam of photons with a minimum energy of 222 kJ/mol can eject electrons from a potassium surface. Estimate the range of wavelengths of light that can be used to cause this phenomenon. Show your calculations with units of measure (dimensional analysis) and briefly explain your reasoning.
Answer: The range of wavelengths of light that can be used to cause given phenomenon is [tex]8.953 \times 10^{21} m[/tex].
Explanation:
Given: 222 kJ/mol (1 kJ = 1000 J) = 222000 J
Formula used is as follows.
[tex]E = \frac{hc}{\lambda}[/tex]
where,
E = energy
h = Planck's constant = [tex]6.625 \times 10^{-25} Js[/tex]
c = speed of light = [tex]3 \times 10^{8} m/s[/tex]
Substitute the values into above formula as follows.
[tex]E = \frac{hc}{\lambda}\\222000 J = \frac{6.625 \times 10^{-34}Js \times 3 \times 10^{8} m/s}{\lambda}\\\lambda = 8.953 \times 10^{21} m[/tex]
Thus, we can conclude that the range of wavelengths of light that can be used to cause given phenomenon is [tex]8.953 \times 10^{21} m[/tex].
2, classify the following molecules as polar or non polar.
A,CH4 B,CHcl C,Co2 D,H2O2 E,BCl3 F,H2S
A. CH4= NON POLAR
B. CH3cl= POLAR
C. CO2= NON POLAR
D. H2O2= POLAR
E. BCl3= NON POLAR
F. H2S= SLIGHTLY POLAR
it takes 513 kj to remove a mole of electrons from the atoms at the surface of a piece of metal. how much energy does it take to remove a single electron from n atom at the surface of the metal
Answer:
The right solution is "[tex]8.5\times 10^{-19} \ joule[/tex]".
Explanation:
As we know,
1 mole electron = [tex]6.023\times 10^{23} \ no. \ of \ electrons[/tex]
Total energy = [tex]513 \ KJ[/tex]
= [tex]513\times 1000 \ joule[/tex]
For single electron,
The amount of energy will be:
= [tex]\frac{513\times 1000}{(6.023\times 10^{23})}[/tex]
= [tex]8.5\times 10^{-19} \ joule[/tex]
2. How many joules of heat are released when 32g of water cools down from 71%
specific heat of water is 4.184 J/gºC)
How many kilojoules is this?
he says he doesnt know sorry
A gas at 74°C is heated to 120°C so there is pressure reaches 1.79 ATM. What is its initial pressure?
Explanation:
here's the answer to your question
For a gas sample containing equimolar amounts of carbon monoxideand heliumat 300 K, heliumhas _____________average speed and _____________ average kinetic energy compared tocarbon monoxidegas.a.a lower; the same b. the same; the same c. a higher; the same d. a higher; higher
Answer:
Option C (a higher; the same) is the appropriate response.
Explanation:
Given:
Temperature,
T = 300 K (both [tex]N_2[/tex] and [tex]H_2[/tex])
As we know,
Average speed of a molecule,
⇒ [tex]\bar v=\sqrt{\frac{8RT}{\pi M} }[/tex]
Thus, the average speed of [tex]N_2[/tex] will be lower as its molar mass is greater than [tex]H_2[/tex].
Now,
⇒ [tex]Average \ kinetic \ energy = \frac{3}{2} \ KT[/tex] (not depend on molar mass)
Hence, it will be the same.
The other three alternatives aren't connected to the scenario given. So the above is the correct answer.
A molecule of acetone and a molecule of propyl aldehyde are both made from 3 carbon atoms, 6 hydrogen atoms, and 1 oxygen atom. The molecules differ in their arrangement of atoms. How do formulas for the two compounds compare? Both compounds have the same molecular formula, but have unique structural formulas. Both compounds have unique molecular formulas and structural formulas. Both compounds have the same structural formula, but have unique molecular formulas.
Explanation:
The structures of both acetone and propanal are shown below:
In the formula of propanal there is -CHO functional group at the end.
In acetone -CO- group is present in the middle that is on the second carbon.
The molecular formula is C3H6O.
Both have same molecular formula but different structural formulas.
