The density of acetonitrile (CH₃CN) is 0.786 g/mL and the density of methanol (CH₃OH) is 0.791 g/mL. A solution is made by dissolving 22.5 mL of CH₃OH in 98.7 mL of CH₃CN. (a) What is the mole fraction of methanol in the solution?

Video transcript

Hi everyone here we have a question telling us that acetone has a density of 0.791 g per million. Ann's island has a density of 0.864 g per milliliter. And it tells us that a solution was prepared by mixing acetone and Xiling our goal here is to calculate the mole fraction of acetone and a solution. If 19.0 mL of acetone was dissolved in 98. millions of Xiling. So first we're going to calculate the moles of acetone. The molar mass of acetone equals 12. g per mole times three for carbon Plus 1.008 g per mole Times six for hydrogen Plus 16 g per mole for oxygen equals 58 . grams per mole. Our moles of acetone equals 19 mL time 0.791 g per mil Leader times one more Divided by 58 .078g. So our middle leaders are canceling out, our g are canceling out. And that gives us 0.259 moles. Now we need to calculate the moles of Xiling. So the molar mass exiling Equals 12.01 g per mole Times eight for carbon Plus 1.008 g per mole times For hydrogen equals 106.16 g per mole. Our moles A Xiling Equals 98.4 ml Times 0.864g. Permanent leader Times one more Over 101.16 g. Our middle leaders are going to cancel out and our g are going to cancel out, giving us 0.840 moles. And now we can calculate the mole fraction. The mole fraction is going to equal the mole of acetone divided by the mole of acetone plus the moles of Xiling so the mole fraction will equal 0.259 moles, Divided by 0.259 moles Plus 0. moles. And that equals 0.236. And that is our final answer. Thank you for watching. Bye.