Question

The density of a gas is measured at 1.653 g/L at 746 mmHg and 25.0 °C. What is its molar mass?

Answer 1

The molar mass of gas is $\boxed{{\text{41}}{\text{.22 g/mol}}}$.

Further Explanation:

An ideal gas is a hypothetical gas that is composed of a large number of randomly moving particles that are supposed to have perfectly elastic collisions among themselves. It is just a theoretical concept and practically no such gas exists. But gases tend to behave almost ideally at a higher temperature and lower pressure.

Ideal gas law is the equation of state for any hypothetical gas. The expression for the ideal gas equation is as follows:

${\text{PV}} = {\text{nRT}}$                               …… (1)

Here,

P is the pressure of the ideal gas.

V is the volume of the ideal gas.

T is the absolute temperature of the ideal gas.

n is the number of moles of gas.

R is the universal gas constant.

The formula to calculate the number of moles of gas is as follows:

${\text{n}} = \frac{{\text{m}}}{{\text{M}}}$                         ...... (2)

Here,

n is the number of moles of gas.

m is the mass of gas.

M is the molar mass of gas.

The formula to calculate the density of the gas is as follows:

${\rho }} = \frac{m}{V}$                              ...... (3)

Here,

${\rho }}$ is the density of the gas.

m is the mass of gas.

V is the volume of gas.

Rearrange equation (3) to calculate the mass of gas.

${\text{m}}={\rho V}}$                                   ...... (4)

Substitute the value of mass from equation (4) in equation (2).

${\text{n}} = \frac{\rho V}{{M}}}$                        ...... (5)

Substitute the value of n from equation (5) in equation (1).

${\text{P}} = \frac{\rho RT}{{\text{M}}}$                           ...... (6)

Rearrange equation (6) to calculate M.

${\text{M}} = \frac{\rho RT}{{\text{P}}}$                         ...... (7)

The density of the gas is 1.653 g/mL.

The pressure of the ideal gas is 746 mm Hg.

The temperature of the ideal gas is ${\text{25}}\;^\circ {\text{C}}$.

The universal gas constant is 0.0821 L atm/K mol.

Substitute these values in equation (7).

$\begin{aligned}{\text{M}}&=\frac{{\left({{\text{1}}{\text{.653 g/mL}}}\right)\left( {0.0821{\text{ L atm/K mol}}}\right)\left({25+27{\text{3}}{\text{.15}}}\right){\text{K}}}}{{\left( {746{\text{ mm Hg}}}\right)\left({\frac{{{\text{1 atm}}}}{{760{\text{ mm Hg}}}}} \right)}} \\&=41.2{\text{216 g/mol}}\\&\approx {\text{41}}{\text{.22 g/mol}}\\\end{aligned}$

Learn more:

1. How many moles of Cl are present in 8 moles of ${\text{CC}}{{\text{l}}_4}$? brainly.com/question/3064603

2. Calculate the moles of ions in HCl solution: brainly.com/question/5950133

Answer details:

Grade: Senior School

Subject: Chemistry

Chapter: Mole concept

Keywords: P, V, n, R, T, ideal gas, pressure, volume, 41.22 g/mol, density, molar mass, 1.653 g/mL, 746 mm Hg, m, M.

Answer 2

Given,

Density of gas = 1.653 g/L
Pressure = 746 mm Hg = 0.981 atm
Temperature = 25 degree Celsius or 298 Kelvin 

By ideal gas law we know,
PV=nRT
where,
P=Pressure
V=Volume of gas
n= no.of moles
R=Universal gas constant (0.0821)
T= temperature
  Now to know the molar mass, we can use following formula;
Molar mass (M) =  mass (m)/ no.of moles(n)
or, No.of moles (n)= mass (m)/Molar mass (M)

also, density is related to mass by formula;
Density = Mass(m) * Volume (V)
o
 Using the above relationship in ideal gas equation, we have,

P.V= m/M. R.T

P. V. M = mRT
M =m /V * RT/P
Since density = m/V, using the relation we get,

M= Density * RT/P
M= (1.653 g/L * 0.082 atm.L/mol.k * 298K)/0.981 atm
  = 41.22 g/mol

Hence the molar mass of the gas is 41.22 g/mol