A sample of iron has a volume of 10.0 mL. The density of iron is 7.87 g/mL. Which is the correct expression to calculate the mass of the sample using dimensional analysis?

10.0 mL Ã (7.87 mL/1 g) 10.0 mL Ã (1 mL/7.87 g) 10.0 mL Ã (1 g/7.87 mL) 10.0 mL Ã (7.87 g/1 mL)

last option: 10 mL * 7.87 g / 1 mL

Explanation:

The dimensional analysis permits you to deduct the correct between the variables that are in direct or inverse relation by looking at the dimensions of each variable and how they can be combined into an equation to yield the desired dimensions (units).

In this case, you have the following quantities with their units:

Volume: 10.0 mL

densitiy: 7.87 g/mL

mass: unknown amount, x, unit: g

Hence, you can state:

g / mL = [mass] / [volume]

7.87 g/mL = x / 10.0 mL

⇒ x = 10 mL * 7.87 g/mL = 10 mL * 7.87 g / 1 mL

That is the last option.