Question

A sample of gas with a mass of 1.45 g occupies a volume of 931 mL at a pressure of 733 Torr and a temperature of 16.0 ∘C . What is the molar mass of the gas?

Answer 1

`38.5\text{ g/mol}`

Step-by-step explanation:

Here, we want to get the molar mass of the gas

Let us call it M

From the ideal gas equation, we can get the number of moles of the gas

Mathematically:

`\begin{gathered} PV\text{ = nRT} \\ n\text{ = }(PV)/(RT) \end{gathered}`

Also, n is the mass divided by the molar mass of the gas:

`\begin{gathered} (m)/(M)\text{ = }(PV)/(RT) \\ \\ M\text{ = }(mRT)/(PV) \end{gathered}`

Where:

M is the molar mass that we want to calculate

m is the mass of the gas sample which is 1.45 g

P is the gas pressure which is 733 torr (to convert to atm, we multiply by 0.00131579 : 733 * 0.00131579 = 0.96 atm)

V is the volume which is 931 mL (We convert to L by dividing by 1000:

931/1000 = 0.931 L)

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

T is the temperature that we convert to K by adding 273 K : 273 + 16 = 289 K)

Substituting the values, we have it that:

`M\text{ = }\frac{1.45\text{ }*0.0821\text{ }*289}{0.96*0.931}\text{ = 38.5 g/mol}`