Question

part a
how many copper atoms are in a pure copper statue with a mass of 165 kg?
express your answer to three significant figures.
cu atoms

Explanation:

Step1: Convert mass to grams

Given mass \(m = 165\space kg\). Since \(1\space kg=1000\space g\), then \(m = 165\times1000\space g=165000\space g\).

Step2: Find the molar mass of copper

The molar mass of copper (\(Cu\)), \(M = 63.55\space g/mol\).

Step3: Calculate the number of moles

Using the formula \(n=\frac{m}{M}\), where \(n\) is the number of moles, \(m\) is the mass, and \(M\) is the molar mass. So \(n=\frac{165000\space g}{63.55\space g/mol}\approx2596.4\space mol\).

Step4: Use Avogadro's number

Avogadro's number \(N_A = 6.022\times 10^{23}\space atoms/mol\). The number of atoms \(N=n\times N_A\). Substitute \(n = 2596.4\space mol\) and \(N_A\) into the formula: \(N=2596.4\times6.022\times 10^{23}\space atoms\).
\(N=(2596.4\times6.022)\times 10^{23}\space atoms\approx1.56\times 10^{27}\space atoms\)

Answer:

\(1.56\times 10^{27}\space Cu\space atoms\)