Question

a brick has a mass of 4.0 kg and the earth has a mass of 6.0×10²⁷ 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? round your answer to 2 significant digits. \boxed{} g how many moles of bricks have a mass equal to the mass of the earth? round your answer to 2 significant digits. \boxed{}

Explanation:

First Sub - Question: What is the mass of 1 mole of bricks?

Step 1: Recall Avogadro's number

Avogadro's number, \(N_A=6.022\times 10^{23}\) (we can use \(6.0\times 10^{23}\) for 2 - significant - figure calculation). The mass of one brick is \(m = 4.0\space kg=4.0\times 10^{3}\space g\) (since \(1\space kg = 1000\space g\)).

Step 2: Calculate the mass of 1 mole of bricks

The mass of 1 mole (which contains \(N_A\) number of bricks) is given by \(M=m\times N_A\). Substituting the values, \(m = 4.0\times 10^{3}\space g\) and \(N_A = 6.0\times 10^{23}\) (for 2 significant figures), we get \(M=(4.0\times 10^{3}\space g)\times(6.0\times 10^{23})=2.4\times 10^{27}\space g\).

Step 1: Identify the mass of the Earth and the mass of 1 mole of bricks

The mass of the Earth, \(M_{Earth}=6.0\times 10^{27}\space g\) and the mass of 1 mole of bricks, \(M = 2.4\times 10^{27}\space g/mol\) (from the first sub - question).

Step 2: Use the formula for moles

The number of moles, \(n=\frac{M_{Earth}}{M}\). Substituting the values, \(n=\frac{6.0\times 10^{27}\space g}{2.4\times 10^{27}\space g/mol}=2.5\space mol\) (rounded to 2 significant figures).

Answer:

\(2.4\times 10^{27}\space g\)

Second Sub - Question: How many moles of bricks have a mass equal to the mass of the Earth?