Question

Which of the following statements about ideal gases is incorrect? At a constant pressure, when temperature increases, volume increases. O A gas with a larger molar mass will have a higher density Gas pressure is directly proportional to the number of moles of gas. At constant volume, when the temperature increases, pressure decreases. At a constant temperature, when the volume decreases, the pressure increases.

Answer 1

1) (d) is incorrect.

a) Correct

From Charles' law: volume of an ideal gas, at constant pressure is directly proportional to the absolute temperature.

I.e. at constant pressure, V_{​​​​​​1} /T​​​​​​_{​​​​​​1} = V₂ /T₂  

b) Correct

From ideal gas equation,

PV = nRT

Where, P = pressure of gas, T = temperature of gas

V = volume of the gas = mass(m) /density (d)

n = no. Of moles of gas = mass(m)/ molar mass (M)

So, P× (m/d) = (m/M) RT

P/d = RT/M

Thus we can see , density of gas is directly proportional to molar mass of the gas.

c) correct

From ideal gas equation: PV = nRT

We see, pressure of gas is directly proportional to no. Of moles of the gas.

d) incorrect

From Gay-lussac's law: at constant volume, pressure of the given amount of the gas is directly proportional to temperature. I.e at constant volume,

P_{​​​​​​1} / T_{​​​​​​1} = P_{​​​​​​2} / T₂  

So, as the temperature increases, pressure also increases.

e) correct

Boyle's law: at constant temperature, volume of the gas is inversely proportional to the pressure of the gas. i.e

At constant temperature,

P1V1 = P2V2

2)

Given, partial pressure of CO_​​​2 , P = 4.55 atm

Volume of container, V = 4.0 L

Temperature, T = 355K

Gas constant , R = 0.0821 L atm^​ mol^{​​​​-1} K^{​​​​​​-1.}

Ideal gas equation : PV= nRT

n = PV/RT

n = (4.55 atm× 4.0L) / (0.0821 L atm mol^{​​​​-1} K^{​​​​​​-1} × 355 K)

= 0.624 moles CO_{^{​​​​​}​​​​​2}

From the given balanced equation,

3 moles of CO2 are produced by = 1 mole C3H8

0.624 moles CO2 will be produced by = 0.624/3 moles C3H8

= 0.208 moles C3H8

Thus moles of C3H8 consumed are 0.208 moles

3) no. of moles of gas, n = 5.46 moles

Volume = 37.1L

Temperature, T = 417K

Gas constant, R = 0.0821 L atm per mol per K

As, PV = nRT

Pressure = P = nRT/V

P = (5.46moles × 0.0821 L atm mol^{​​​​-1}​​ K^{​​​​​​-1} × 417K )/37.1L

= 5.04 atm

Pressure of gas = 5.04 atm