Question

problem: the mass per unit volume of a pure substance is defined to be its density. calculate the volume of 3.5 kg of a liquid with a measured density of 678 g/l. be sure your answer has a unit symbol and the correct number of significant digits. solution: write down the definition of density. (p=\frac{m}{v}) solve for volume. (v = \frac{m}{p}) put in the data given. (m = 3.5 kg), (p=678 g/l) convert units. (3.5 kg=\frac{3.5 kg}{1}left(\frac{10^{3}g}{1 kg}
ight)) (v=\frac{3.5 kg}{678 g/l}) use the calculator. (v = 5.162cdots l) round to the correct number of significant digits. (v = 5.2 l) no mistakes

Explanation:

Step1: Write the density - volume - mass formula

The density formula is $
ho=\frac{m}{V}$, where $
ho$ is density, $m$ is mass and $V$ is volume. We need to solve for $V$, so we can re - arrange the formula to $V = \frac{m}{
ho}$.

Step2: Convert the units

The mass $m = 3.5\ kg$. Since $1\ kg=10^{3}\ g$, then $m = 3.5\times10^{3}\ g$. The density $
ho=678\ g/L$.

Step3: Substitute the values into the formula

Substitute $m = 3.5\times 10^{3}\ g$ and $
ho = 678\ g/L$ into $V=\frac{m}{
ho}$. So $V=\frac{3.5\times 10^{3}\ g}{678\ g/L}$.

Step4: Calculate the volume

Using a calculator, $V=\frac{3.5\times 10^{3}}{678}\ L\approx5.16\ L$.

Answer:

$5.2\ L$ (rounded to two significant digits)