Question

a sample of calcium has a volume of 10.0 ml. the density of calcium is 1.55 g/ml. which is the correct expression to calculate the mass of the sample using dimensional analysis?

Answer 1

D = m/v
1.55 g/ml = 1.55 g/1ml

m = dv

1ml x 1.55 g/ml =1.55 g

Answer 2

Answer:

mass = volume x density

Explanation:

In the dimensional analysis the units can be viewed as algebraic objects and can be treated as variables in an equation. This is used to make sure that the results are shown in the actual units, so one knows the calculation is correct.

In this exercise they are asking for the mass of a sample of calcium and we know that the most common mass unit is the grams (g), then the result should be in this unit.

Notice that if we multiply the volume time the density the units of volume, that is mL, will cancel out and the units left are grams, like this:

$mass = (10.0 mL) (1.55\frac{g}{mL}) = (10.0)(1.55)(mL)(\frac{g}{mL} ) = 15.5 g$

So the correct expression to calculate the mass of the sample is mass = volume x density