Questions: States of Matter Calculating mole fraction in a gas mixture A 10.00 L tank at 22.2 °C is filled with 19.0 g of sulfur hexafluoride gas and 8.88 g of boron trifluoride gas. You can assume both gases behave as ideal gases under these conditions. Calculate the mole fraction of each gas. Be sure each of your answer entries has the correct number of significant digits. gas mole fraction sulfur hexafluoride [] boron trifluoride []

Solution Steps

First, we need to calculate the number of moles of sulfur hexafluoride (SF\(_6\)) and boron trifluoride (BF\(_3\)) using their respective molar masses.

The molar mass of SF\(_6\) is: \[ \text{Molar mass of SF}_6 = 32.07 + 6 \times 18.998 = 146.07 \, \text{g/mol} \]

The molar mass of BF\(_3\) is: \[ \text{Molar mass of BF}_3 = 10.81 + 3 \times 18.998 = 67.81 \, \text{g/mol} \]

Now, calculate the number of moles of each gas: \[ \text{Moles of SF}_6 = \frac{19.0 \, \text{g}}{146.07 \, \text{g/mol}} = 0.1300 \, \text{mol} \] \[ \text{Moles of BF}_3 = \frac{8.88 \, \text{g}}{67.81 \, \text{g/mol}} = 0.1309 \, \text{mol} \]

Add the moles of both gases to find the total number of moles: \[ \text{Total moles} = 0.1300 \, \text{mol} + 0.1309 \, \text{mol} = 0.2609 \, \text{mol} \]

The mole fraction of a gas is given by the ratio of the number of moles of that gas to the total number of moles in the mixture.

For SF\(_6\): \[ \text{Mole fraction of SF}_6 = \frac{0.1300 \, \text{mol}}{0.2609 \, \text{mol}} = 0.4981 \]

For BF\(_3\): \[ \text{Mole fraction of BF}_3 = \frac{0.1309 \, \text{mol}}{0.2609 \, \text{mol}} = 0.5019 \]

Final Answer