Question

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1. the mineral cuprite consists of 88.8% cu and 11.2% o by mass; determine the empirical formula of cuprite.

Explanation:

Step1: Calculate the moles of each element

Assume we have a 100 - g sample of cuprite. Then the mass of \(Cu\) is \(m_{Cu}=88.8\ g\) and the mass of \(O\) is \(m_{O} = 11.2\ g\).
The molar mass of \(Cu\) is \(M_{Cu}=63.55\ g/mol\), and the molar mass of \(O\) is \(M_{O}=16.00\ g/mol\).
The number of moles of \(Cu\), \(n_{Cu}=\frac{m_{Cu}}{M_{Cu}}=\frac{88.8\ g}{63.55\ g/mol}\approx1.4\ mol\)
The number of moles of \(O\), \(n_{O}=\frac{m_{O}}{M_{O}}=\frac{11.2\ g}{16.00\ g/mol}= 0.7\ mol\)

Step2: Find the mole ratio

Divide each number of moles by the smaller number of moles (\(n = 0.7\ mol\))
For \(Cu\): \(\frac{n_{Cu}}{n}=\frac{1.4\ mol}{0.7\ mol}=2\)
For \(O\): \(\frac{n_{O}}{n}=\frac{0.7\ mol}{0.7\ mol}=1\)

Answer:

The empirical formula of cuprite is \(Cu_{2}O\)