Question

An experiment shows that a 112 mL gas sample has a mass of 0.170 g at a pressure of 721 mmHg and a temperature of 30 ∘C What is the molar mass of the gas?

Answer 1

`39.5\text{ g/mol}`

Step-by-step explanation:

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

We start by getting the number of moles of the gas used in the experiment

We can get this bu using the ideal gas equation as follows;

`\begin{gathered} PV\text{ = nRT} \\ where: \\ P\text{ is the preesure, given as 721 mmHg} \\ V\text{ is the volume of the gas which is 112 mL = 0.112 L } \\ T\text{ is the temperature which is 30 + 273.15 = 303.15 K }(to\text{ absolute scale}) \\ n\text{ is the number of moles that we want to calculate} \\ R\text{ is 0.0821 L atm}^\text{ K}^(-1)\text{ mol}^(-1) \end{gathered}`

Before we use these values, we have to convert Pressure to atm (We can do this by dividing the pressure value by 760

`721\text{ mmHg = }(721)/(760)\text{ = 0.9487 atm}`

Substituting the values, we have:

`\begin{gathered} 0.9487*0.112\text{ = n}*0.0821*303.15 \\ n\text{ = }(0.9487*0.112)/(0.0821*303.15)\text{ = 0.0043 mol} \end{gathered}`

To get the molar mass of the gas, we have to divide the mass by the number of moles of the gas used in the experiment

Mathematically, we have that as:

`(0.170)/(0.0043)\text{ = 39.5 g/mol}`