Question

A 29.5 g sample of nitrogen, N2, has a volume of 50.0 L and a pressure of 550. mmHg.What is the temperature of the gas in kelvins?Express your answer to three significant figures.

Answer 1

`418\text{ K}`

Step-by-step explanation:

Here, we want to get the temperature of the gas

Mathematically, from the ideal gas equation:

`\begin{gathered} PV\text{ = nRT} \\ T\text{ = }(PV)/(nR) \end{gathered}`

where:

T is the temperature that we want to calculate

V is the volume given as 50 L

n is the number of moles that we can get by dividing the given mass by the molar mass of N2 (The molar mass of N2 is 28 g/mol: thus, we have the number of moles as 29.5/28 = 1.054 mol)

P is the pressure which we have to convert to atm by dividing by 760 mm Hg: we have that as 550/760 = 0.724 atm)

R is the molar gas constant which is 0.0821 L.atm/mol.K

Substituting the values, we have it that:

`T\text{ = }(0.724*50)/(1.054*0.0821)\text{ = 418K}`