Question

A sample of an unknown gas with a molar mass of 85.74 is placed in a vessel with avolume of 1,681 mL at a temperature of 58.6 °C. If the pressure is 5.4 atm, howmany grams of this gas are present?

Answer 1

28.58 grams

Step-by-step explanation

Given:

Molar mass of the gas, M = 85.74 g/mol

Volume, V = 1,681 mL = 1.681 L

Temperature, T = 58.6 °C = (58.6 + 273.15 K) = 331.75 K

Pressure, P = 5.4 atm

What to find:

The mass of the gas in grams present.

Step-by-step solution:

The mass in grams of the gas present can be calculated using the ideal gas equation:

`\begin{gathered} PV=nRT \\ \\ n=moles=\frac{Mass}{Molar\text{ }mass} \\ \\ \Rightarrow PV=\frac{Mass}{Molar\text{ }mass}RT \end{gathered}`

Putting the values of the given parameters and R = 0.0821 atm•L/mol•K into the formula:

`\begin{gathered} 5.4atm*1.681L=\frac{Mass}{85.74g\text{/}mol}*0.0821atm•L/mol•K*331.75K \\ \\ 9.0774atm•L=Mass(0.317665908atm•L/g) \\ \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }0.317665908atm•L/g \\ \\ (9.0774atm•L)/(0.317665908atm•L/g)=\frac{Mass(0.317665908atm•L)}{0.317665908atm•L\text{/}g} \\ \\ \Rightarrow Mass=28.58\text{ }grams \end{gathered}`

The mass of the gas in grams present = 28.58 grams.