Questions: A brick has a mass of 4.0 kg and the Earth has a mass of 6.0 x 10^27 g. Use this information to answer the questions below. Be sure your answers have the correct number of significant digits. What is the mass of 1 mole of bricks? How many moles of bricks have a mass equal to the mass of the Earth? 2.5

Solution Steps

To find the mass of 1 mole of bricks, we use Avogadro's number, which is \(6.022 \times 10^{23}\) entities per mole. Given that the mass of one brick is 4.0 kg, the mass of 1 mole of bricks is calculated as follows:

\[ \text{Mass of 1 mole of bricks} = 4.0 \, \text{kg/brick} \times 6.022 \times 10^{23} \, \text{bricks/mole} \]

\[ = 2.4088 \times 10^{24} \, \text{kg/mole} \]

The mass of the Earth is given as \(6.0 \times 10^{27} \, \text{g}\). We need to convert this mass into kilograms:

\[ \text{Mass of Earth in kg} = 6.0 \times 10^{27} \, \text{g} \times \frac{1 \, \text{kg}}{1000 \, \text{g}} = 6.0 \times 10^{24} \, \text{kg} \]

To find how many moles of bricks have a mass equal to the mass of the Earth, we divide the Earth's mass by the mass of 1 mole of bricks:

\[ \text{Number of moles of bricks} = \frac{6.0 \times 10^{24} \, \text{kg}}{2.4088 \times 10^{24} \, \text{kg/mole}} \]

\[ = 2.4908 \approx 2.5 \, \text{moles} \]

Final Answer