A gas has a density of 2.22 g/L at 1.04 atm and a molar mass of 51.7 g/mol.
What is the temperature of the gas in Kelvin?
.

295.4K

Explanation:

Step 1:

Obtaining an expression which relates density, pressure and temperature together.

This is can done by using the ideal gas equation as shown below:

PV = nRT (1)

Recall:

Number of mole (n) = mass (m) /Molar Mass (M) i.e

n = m/M

Substituting the m/M for n in equation 1 above

PV = nRT

PV = mRT/M

Divide both side by P

V = mRT/MP

Divide both side by m

V/m = RT/MP

Invert the above equation

m/V = MP/RT(2)

Density (D) = mass (m) /volume (V)

D = m/V

Replacing m/V with D in equation 2.

m/V = MP/RT

D = MP/RT

Step 2:

Data obtained from the question. This includes the following:

Density (D) = 2.22 g/L

Pressure (P) = 1.04 atm

Molar Mass of (M) = 51.7 g/mol.

Temperature (T) =.?

Gas constant (R) = 0.082atm.L/Kmol

Step 3:

Determination of the temperature.

D = MP/RT

2.22 = 51.7 x 1.04 / 0.082 x T

Cross multiply to express in linear form

2.22 x 0.082 x T = 51.7 x 1.04

Divide both side by 2.22 x 0.082

T = (51.7 x 1.04) /(2.22 x 0.082)

T = 295.4K

Therefore, the temperature of the gas is 295.4K

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