A solution is prepared by dissolving 20.2 mL of methanol (CH₃OH) in 100.0 mL of water at 25 °C. The final volume of the solution is 118 mL. The densities of methanol and water at this temperature are 0.782 g/mL and 1.00 g/mL, respectively. For this solution, calculate the concentration in each unit. c. percent by mass

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Hey everyone, we're told that at 25°C, 100 ml of isopropyl alcohol was mixed with 42.9 ml of water to create a solution at the same temperature. The densities of isopropyl alcohol and water are 0.781 g per milliliter and 1.0 g per milliliter respectively. What is the concentration of the solution in percent by mass. To answer this question, we're going to have to use the following formula, which is going to be density equals mass over volume. And first we want to solve for the mass of isopropyl alcohol and the mass of our water. So we're going to rearrange this into mass is equal to density times our volume. So solving for the mass of isopropyl alcohol, we're going to take our density which is said to be 0.781 g per milliliter. And we're going to multiply it by our volume, which was said to be 100 ml. Now, when we calculate this out, we end up with a mass of 78.1 g. Now, let's go ahead and calculate the mass of our water. We're going to take the same steps and take our density, which is said to be 1.0 g per millimeter And multiply it by its volume of 42.9 ml. This will get us to a mass of 42.9 g. Now we can go ahead and add these two values up to get our total mass. So we have 78.1 g plus 42. g, Which gets us to a total of 121 g. Now to solve for our percent of our isopropyl by mass, we're going to use the following formula which is going to be our mass of our isopropyl divided by our total mass. And we're going to multiply this by 100%. Since we are looking for a percentage. So plugging in these values, we get 78.1 g divided by 121 g. And we're going to multiply this by 100% And this gets us to a percent mass of 64.5%. Which is going to be our final answer. Now, I hope this made sense. And let us know if you have any questions.

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Key Concepts

Concentration Units

Density and Mass Calculation

Final Volume of Solution