Question

A sample of iron has a volume of 10.0 mL. The density of iron is 7.87 g/mL. Which is thecorrect expression to calculate the mass of the sample using dimensional analysis?a. 10.0 mL x 7.87g/1mL b. 10.0 mL x 1g/7.87mL c. 10.0 mL x 1mL/7.87gd. 10.0 mL x 7.87mL/1g

Answer 1

• option a. 10.0 mL × 7.87 g / 1mL

Step-by-step explanation:

The symbol [ ] is used to indicate units, so:

• [m] means mass units

• [V] means volume units

• [d] means density units

Here:

• [m] = g

• [V] = mL

• [d] = g/ mL

Since, you know the volume of the sample (10.0 mL), the density of the iron (7.87 g/mL), and you need to find the expression to calculate the mass of the sample, you use dimensional analysis:

• g = mL × g / mL ← here you see that in the right side mL of the first factor cancels with mL in the denominator of the second factor, yielding g, with which the units of the left side and the right side are equal.

• Then, you just must add the numerical values for each group of units:

g = 10.0 mL × 7.87 g / mL is the desired expression.

When you simplify that expression you obtain:

• g = 78.7 g ↔ [ mL were canceled]. And that is the mass of the sample of iron applying dimensional analysis to the given data.