Calculate the mass of copper liberated by one coulomb of charge if 0.48 g of copper is liberated by a current of 400 A flowing for 1 hour.

The given time is one hour.

$$t = 1 \text{ hour} \times 60 \frac{\text{minutes}}{\text{hour}} \times 60 \frac{\text{seconds}}{\text{minute}} = 3600 \text{ s}$$

The formula for charge is $Q = I \times t$, where $I$ is the current and $t$ is the time.
The given current is $I = 4.0 \times 10^2 \text{ A}$.

$$Q = (4.0 \times 10^2 \text{ A}) \times (3600 \text{ s})$$ $$Q = 400 \text{ A} \times 3600 \text{ s}$$ $$Q = 1,440,000 \text{ C}$$ $$Q = 1.44 \times 10^6 \text{ C}$$

The problem states that $0.48 \text{ g}$ of copper was liberated by $1.44 \times 10^6 \text{ C}$ of charge. To find the mass liberated by one coulomb, divide the total mass liberated by the total charge.

$$\text{Mass per coulomb} = \frac{\text{Mass of copper liberated}}{\text{Total charge passed}}$$ $$\text{Mass per coulomb} = \frac{0.48 \text{ g}}{1.44 \times 10^6 \text{ C}}$$ $$\text{Mass per coulomb} = 3.333... \times 10^{-7} \text{ g/C}$$ $$\text{Mass per coulomb} \approx 3.33 \times 10^{-7} \text{ g/C}$$

The mass of copper liberated by one coulomb of charge is $\mathbf{3.33 \times 10^{-7} \text{ g}}$.