Question

1. for the masses and volumes indicated, calculate the density to grams per cubic centimeters.

a. mass = 452.1 g; volume = 292 cm³
b. mass = 0.14 lb; volume = 125 ml
c. mass = 1.01 kg; volume = 1000 cm³
d. mass = 225 mg; volume = 2.51 ml

Explanation:

Step1: Recall density formula

The formula for density $
ho$ is $
ho=\frac{m}{V}$, where $m$ is mass and $V$ is volume. We need to convert mass to grams and volume to $cm^{3}$ if necessary (since $1\ mL = 1\ cm^{3}$).

Step2: Solve for part a

• Given $m = 452.1\ g$ and $V=292\ cm^{3}$.
• Using the density formula $

ho=\frac{m}{V}$, we substitute the values: $
ho=\frac{452.1\ g}{292\ cm^{3}}\approx1.55\ g/cm^{3}$.

Step3: Solve for part b

• First, convert mass from pounds to grams. Since $1\ lb = 453.592\ g$, then $m = 0.14\ lb\times453.592\ g/lb\approx63.50\ g$.
• Given $V = 125\ mL=125\ cm^{3}$.
• Using the density formula $

ho=\frac{m}{V}$, we have $
ho=\frac{63.50\ g}{125\ cm^{3}}\approx0.51\ g/cm^{3}$.

Step4: Solve for part c

• Convert mass from kilograms to grams. Since $1\ kg=1000\ g$, then $m = 1.01\ kg\times1000\ g/kg = 1010\ g$.
• Given $V = 1000\ cm^{3}$.
• Using the density formula $

ho=\frac{m}{V}$, we get $
ho=\frac{1010\ g}{1000\ cm^{3}} = 1.01\ g/cm^{3}$.

Step5: Solve for part d

• Convert mass from milligrams to grams. Since $1\ g = 1000\ mg$, then $m=225\ mg\times\frac{1\ g}{1000\ mg}=0.225\ g$.
• Given $V = 2.51\ mL = 2.51\ cm^{3}$.
• Using the density formula $

ho=\frac{m}{V}$, we obtain $
ho=\frac{0.225\ g}{2.51\ cm^{3}}\approx0.09\ g/cm^{3}$.

Answer:

a. $\approx1.55\ g/cm^{3}$
b. $\approx0.51\ g/cm^{3}$
c. $1.01\ g/cm^{3}$
d. $\approx0.09\ g/cm^{3}$