Question

An empty 250 mL beaker has a mass of 60 g. When 100 mL of oil is added to the beaker, the total mass is 140 g. What is the density of the oil?

Answer 1

`"0.8 g mL"^(-1)`

Explanation:

To find the density of the oil, all you have to do is figure out how many grams you get in `"1 mL"` of oil.

In that regard, the density of a substance is simply the mass of one unit of volume of said substance. Since you're working with milliliters here, the mass of one unit of volume will be the mass of `"1 mL"` of oil.

Now, you know that the empty beaker has a mass of `"60 g"`. After you add the oil, its mass increases to `"140 g"`. This means that the mass of the oil will be

`m_"oil" = "140 g" - "60 g" = "80 g"`

Notice that you don't need to know the volume of the empty beaker to find the density of the oil; since you already know the mass of the oil, all you need to know is its volume.

The problem states that you're adding `"100 mL"` of oil to the beaker. Well, if `"100 mL"` of oil have a mass of `"80 g"`, it follows that `"1 mL"` of oil will have a mass of

`1 color(red)(cancel(color(black)("mL"))) * "80 g"/(100color(red)(cancel(color(black)("mL")))) = "0.80 g"`

This means that the density of the oil, `rho`, is equal to

`color(darkgreen)(ul(color(black)(rho = "0.8 g mL"^(-1)))) ->` every milliliter of oil has a mass of `"0.8 g"`

The answer is rounded to one significant figure.