Question

If there is a mixture of hydrogen and oxygen gas in a container with 10 moles total and the mole fraction of hydrogen is .67, how many moles of each gas are there?

Answer 1

The number of moles of hydrogen is 6.7 moles

The number of moles of oxygen is 3.3 moes

Step-by-step explanation

Given that;

The total number of moles of gases is 10

The mole fraction of hydrogen is 0.67

Follow the steps below to find the number of moles of each gas

Recall, that the total mole fractions all of the gases in container must be 1

Mathematically

Mole fraction of hydrogen + mole fraction of oxygen = 1

The next step is to find the mole fraction of oxygen

`\begin{gathered} \text{ Mole fraction of hydrogen + mole fraction of oxygen = 1} \\ \text{ 0.67 + mole fraction of oxygen = 1} \\ \text{ Subtract 0.67 from both sides of the equation} \\ \text{ 0.67 - 0.67 + mole fraction of oxygen = 1} \\ \text{ mole fraction of oxygen = 1 - 0.67} \\ \text{ Mole fraction of oxygen = 0.33} \end{gathered}`

The mole fraction of oxygen is 0.33

The next step os to find the number of moles of each gas in the container using the below formula

`\text{ mole fraction = }\frac{\text{ number of moles of gas}}{\text{ total number of moles of the gases}}`

For hydrogen gas

`\begin{gathered} \text{ 0.67 = }\frac{\text{ number of moles of hydrogen}}{\text{ 10}} \\ \text{ cross multiply} \\ \text{ number of moles of hydrogen gas = 0.67 }*\text{ 10} \\ \text{ number of moles of hydrogen gas = 6.7 moles} \end{gathered}`

Therefore, the number of moles of hydroges gas in the mixture is 6.7 moles

For oxygen

`\begin{gathered} \text{ 0.33 = }\frac{\text{ number of moles of oxygen}}{\text{ 10}} \\ \text{ cross multiply} \\ \text{ number of moles of oxygen = 0.33 }*\text{ 10} \\ \text{ number of moles of oxygen = 3.3 moles} \end{gathered}`

The number of moles of oxygen is the mixture is 3.3 moles