Solutions and cognitive properties

Question

A solution is made using 200.00ml of methanol (density 0.7920 g/ml) and 907.1 ml of water (density 1.00 g/ml). What is the mass percent of methanol?

Answer 1

First, remember that the question asks for mass percent. The word "mass" refers to grams. So we are going to have to convert the amounts of methanol and water ( both of which were given in mL) to grams. The problem gave you the densities of both methanol and water, so we have all the info we need.

Follow the steps shown below to solve this problem (and any other mass percent problem like this one).

Step 1: Look at the equation below for converting mL to grams if you are given density. Remember this equation.

Grams of a substance = amount of the substance in mL x density of the substance

Step 2: Find the information given in the problem about the mL of methanol and the density of methanol

The problem says that we have 200.00 mL of methanol. (We can just write this as 200 mL to make it easier.) The problem also says that the density of methanol is 0.7920 g/mL.

Step 3: Put the numbers we found in Step 2 into the equation I gave you in Step 1:

Since we are solving for grams of methanol, we can write the equation from Step 1 like this:

Grams of methanol = mL of methanol x density of methanol

We know from Step 2 that mL of methanol = 200 mL and density of methanol = 0.7920 g/mL. We put these numbers in the equation so the equation looks like this:

Grams of methanol = 200 x 0.7920

Step 4: Solve for the grams of methanol

We use a calculator to do 200 x 0.7920. The calculator says that 200 x 0.7920 = 158.4. So we have 158.4 grams of methanol.

Step 5: Find the information given in the problem about the mL of water and the density of water

Now we need to convert the mL of water into grams of water. We start by finding the information about the mL of water and the density of water. The problem says that we have 907.1 mL of water and the density of water is 1.00 g/mL. (We can write the density of water as 1 to make it simpler; it's the same thing.)

Step 6: Put the numbers we found in Step 5 into the equation I gave you in Step 1:

Since we are solving for grams of water, we can write the equation from Step 1 like this:

Grams of water = mL of water x density of water

We know from Step 5 that mL of water = 907.1 mL and density of methanol = 1 g/mL. We put these numbers in the equation so the equation looks like this:

Grams of water = 907.1 x 1

Step 7: Solve for the grams of water

To find the grams of water, we do 907.1 x 1. 907.1 x 1 = 907.1. So we have 907.1 grams of water.

Step 8: Look at this equation for finding the mass percentage of methanol. Remember this equation:

Mass percentage of methanol = ( Grams of methanol / Total grams ) x 100

Step 9: Find the Total grams by adding together the grams of methanol and the grams of water

In other words, Total grams = grams of methanol + grams of water . We know from Step 4 that we have 158.4 grams of methanol. We also know from Step 7 that we have 907.1 grams of water. So we do:

Total grams = 158.4 + 907.1

We use a calculator to do 158.4 + 907.1. The calculator says that 158.4 + 907.1 = 1,065.5 .

So the Total grams = 1,065.5

Step 10: Put the information about the grams of methanol and the Total grams in the equation for the Mass Percentage

Mass percentage of methanol = (158.4 / 1065.5 ) x 100

Step 11: Use a calculator to calculate 158.4 / 1065.5

We use a calculator to do 158.4 / 1065.5 . The calculator says that 158.4 / 1065.5 = 0.1487.

Step 12: Put the number we found in Step 11 into the equation for Mass Percentage:

Mass percentage of methanol = 0.1487 x 100

Step 13: Multiply 0.1487 x 100 to find the Mass Percentage

We use a calculator to do 0.1487 x 100. The calculator says that 0.1487 x 100 = 14.87. We add the percent sign (%) after this number because we always add the percent sign when asked for a percentage. So the Mass Percentage of methanol = 14.87%.

Final Answer: The Mass Percentage of methanol is 14.87%.