Question Video: Determining a Formula Used to Calculate the Volume of a Substance Given the Mass and Density Chemistry

Video Transcript

The density of a substance can be calculated using the following equation: density equals mass divided by volume. What is the formula for calculating the volume of a substance when given the mass and density?

In this equation for density, the density is isolated on the left-hand side, which makes density the subject of this equation. The subject in a mathematical formula is the isolated term. It is the variable that’s being solved for. It does not matter if the subject is on the left- or the right-hand side of the equation. The subject of an equation can be changed by rearranging the formula. This is what we need to do in this question. We need to rearrange the formula for density so that the volume is the subject of the equation. That way we can solve for the volume if we are given the mass and density.

Before rearranging our formula, we should understand two rules. The first is that whatever is done to one side of the equation must be done to the other side as well. That is, if we are adding something, we need to add the same thing to the other side. If we multiply by something, we need to multiply on the other side as well. For example, if we want to solve for 𝑥, we would divide the left-hand side by 10, so the 10s will cancel, and we can isolate 𝑥 on the left-hand side of the equation. But we’ll also need to divide the right-hand side of the equation by 10 as well. That way, we can solve for 𝑥 and discover that 𝑥 equals five.

The second rule is that we can cancel or move a quantity or variable if we perform the opposite operation to both sides of the equation. Addition and subtraction cancel each other, as do multiplication and division. For example, if we have the equation 𝑎 plus 𝑏 equals 𝑐, if we would like 𝑎 to be the subject of the equation, we will need to move 𝑏 to the other side of the equation. Since 𝑏 is being added to 𝑎, we can move 𝑏 to the right-hand side of the equation if we subtract 𝑏 from both sides, This will cancel 𝑏 on the left-hand side of the equation. We are left with 𝑎 equals 𝑐 minus 𝑏, where 𝑎 is the subject of the equation.

Now let’s apply these rules to solve for the volume. The easiest way to isolate the volume would be to divide both sides of the equation by the mass. This would cause the mass to cancel, isolating the volume on the right-hand side of the equation. But the subject of an equation needs to be in the numerator, not the denominator like it is here. So we need to use a different strategy.

Since the mass is being divided by the volume, we can multiply both sides of the equation by the volume to move the volume to the other side. This will cancel the volume on the right-hand side of the equation. Now, we need to isolate the volume on the left-hand side. We can do this if we divide both sides of the equation by the density. This will cancel the density on the left-hand side of the equation, leaving the volume isolated on the left-hand side.

Now, the volume is the subject of the equation, so we’ve solved the problem. The formula for calculating the volume of a substance when given the mass and density is volume equals mass divided by density.