Question

density calculations worksheet
density = mass / volume
units of density
solids (g/cm³) liquids (g/ml)

1. find the unknown quantity:

a) d = 3 g/ml
v = 100ml
m =
b) d =
v = 950ml
m = 95g
c) d = 0.5 g/cm³
v =
m = 20g

1. find the unknown quantity (convert first to g or ml)

a) d = 24 g/ml
v = 1.2l = ______ml
m =
b) d =
v = 100ml
m = 1.5kg = ______g
c) d =
v = 0.52l = ______ml
m = 500 mg = ______g

Explanation:

Step1: Recall density formula

The formula is $d=\frac{m}{V}$, where $d$ is density, $m$ is mass and $V$ is volume.

Step2: Solve part 1A

Given $d = 3\ g/mL$ and $V=100\ mL$. Using $m = d\times V$, we have $m=3\ g/mL\times100\ mL = 300\ g$.

Step3: Solve part 1B

Given $V = 950\ mL$ and $m = 95\ g$. Using $d=\frac{m}{V}$, we get $d=\frac{95\ g}{950\ mL}=0.1\ g/mL$.

Step4: Solve part 1C

Given $d = 0.5\ g/cm^{3}$ and $m = 20\ g$. Using $V=\frac{m}{d}$, we have $V=\frac{20\ g}{0.5\ g/cm^{3}} = 40\ cm^{3}$.

Step5: Convert units for part 2A

Since $1\ L=1000\ mL$, then $V = 1.2\ L=1.2\times1000\ mL = 1200\ mL$. Given $d = 24\ g/mL$, using $m = d\times V$, we get $m=24\ g/mL\times1200\ mL=28800\ g$.

Step6: Convert units for part 2B

Since $1\ kg = 1000\ g$, then $m = 1.5\ kg=1.5\times1000\ g = 1500\ g$. Given $V = 100\ mL$, using $d=\frac{m}{V}$, we have $d=\frac{1500\ g}{100\ mL}=15\ g/mL$.

Step7: Convert units for part 2C

Since $1\ L = 1000\ mL$, then $V = 0.52\ L=0.52\times1000\ mL = 520\ mL$. Since $1\ g=1000\ mg$, then $m = 500\ mg=\frac{500}{1000}\ g=0.5\ g$. Using $d=\frac{m}{V}$, we get $d=\frac{0.5\ g}{520\ mL}\approx0.00096\ g/mL$.

Answer:

1A. $m = 300\ g$
1B. $d = 0.1\ g/mL$
1C. $V = 40\ cm^{3}$
2A. $V = 1200\ mL$, $m = 28800\ g$
2B. $m = 1500\ g$, $d = 15\ g/mL$
2C. $V = 520\ mL$, $m = 0.5\ g$, $d\approx0.00096\ g/mL$