Answer to Question #145112 in General Chemistry for liam donohue

Question

Determine the density of methane at 1.000atm of pressure and a temperature of 0.000 degrees. The gas constant R=0.0821L

d(0 degrees)=
d (-33 degrees)=
Based on the gas law equations that are used to solve density, what is the unit of d=

Answer 1

We know the ideal gas equation

PV=nRT

P = pressure of the gas

T = temperature of gas

V = volume occupied by the gas

Number of mole, n = W/M

W = total weight of the gas in the system

M = molar mass of gas

So, the ideal gas equation can be written as

PV = (W/M)RT

Or, PM = (W/V)RT

Or, PM = dRT

Or, d = PM/RT

Where, density of the gas = D = (W/V)

Given,

The gas constant R=0.0821L

Pressure, P = 1.000atm

Molar mass of methane gas,M = 16g/mol

So, at temperature = 0°C

i.e. T = 273 K

Density of gas, d = (1×16)/(0.082×273)

= 0.715 g/L

The density of the gas,

d(0 degrees)=0.715 g/L

at temperature = -33°C

T = (273-33)K

= 240 K

Density of gas, d = (1×16)/(0.082×240)

= 0.813 g/L

The density of the gas,

d(-33 degrees) = 0.813 g/L