Question

A 10.0 g sample of a gas occupies 7.69 L at 1.00 atm and 27.0 C. The gas has been determined to be diatomic. What is the gas

Answer 1

Step-by-step explanation

Given that

The mass of the gas is 10.0g

The volume of the gas is 7.69L

The pressure of the gas is 1.00 atm

The temperature of the gas is 27 degrees Celcius

Follow the steps below to find the molar mass of the gas

Step1; Assume the gas is an ideal gas

`\text{ Pv = nRT}`

Step 2; Find the number of mole of the gas using the equation above

`\begin{gathered} \text{ T K = t}\degree C\text{ + 273.15} \\ \text{ T K = 27 + 273.15} \\ \text{ T K = 300.15K} \end{gathered}`
`\begin{gathered} \text{ R is 0.0825 L.atm . K}^(-1)\text{ mol}^(-1) \\ \text{ 1 }*\text{ 7.69 = n }*\text{ 300.15 }*\text{ 0.08205} \\ \text{ 7.69 = n24.627} \\ \text{ Divide both sides by 24.627} \\ \text{ n = }(7.69)/(24.627) \\ \text{ n = 0.312 moles} \end{gathered}`

Step 3; find the molar mass of the sample

`\begin{gathered} \text{ mole = }\frac{\text{ mass}}{molar\text{ mass}} \\ \text{ cross multiply} \\ \text{ mass = mole x molar mass} \\ \text{ molar mass =}\frac{mass}{\text{ mole}} \\ \\ \text{ molar mass = }(10)/(0.312) \\ \text{ molar mass = 32.05} \end{gathered}`