Question

10 a sample contains 5.5 × 10²⁴ atoms of cadmium. what is the mass of the sample (round to whole number) in grams? blank box

Explanation:

Step1: Recall Avogadro's number and molar mass of calcium

Avogadro's number is \( 6.022\times 10^{23}\) atoms/mol, and the molar mass of calcium (Ca) is approximately \( 40.08\space g/mol\).

Step2: Calculate moles of calcium

Moles (\(n\)) = Number of atoms / Avogadro's number. So \(n=\frac{5.5\times 10^{24}\space atoms}{6.022\times 10^{23}\space atoms/mol}\approx 9.13\space mol\)

Step3: Calculate mass of calcium

Mass (\(m\)) = Moles (\(n\)) × Molar mass (\(M\)). So \(m = 9.13\space mol\times40.08\space g/mol\approx 366\space g\) (or more precisely, let's do the calculation with more accuracy)

First, \(n=\frac{5.5\times 10^{24}}{6.022\times 10^{23}}=\frac{5.5}{6.022}\times 10^{24 - 23}=\frac{5.5}{6.022}\times 10\approx0.913\times 10 = 9.13\space mol\)

Then, \(m=9.13\space mol\times40.08\space g/mol = 9.13\times40.08\approx 366\space g\) (if we use more precise calculation: \(5.5\times 10^{24}\div6.022\times 10^{23}= (5.5\div6.022)\times 10^{24 - 23}\approx0.913\times 10 = 9.13\) moles. Then \(9.13\times40.078 = 9.13\times40+9.13\times0.078=365.2+0.712 = 365.912\approx 366\space g\))

Answer:

The mass of the sample of calcium is approximately \(\boldsymbol{366\space g}\) (or if we consider more precise steps, it can be calculated as follows: \(n=\frac{5.5\times 10^{24}}{6.022\times 10^{23}} = \frac{5.5}{6.022}\times 10\approx9.13\space mol\), \(m = 9.13\space mol\times40.08\space g/mol\approx 366\space g\))