Question

heating 4.05 g of a metal oxide (molar mass of metal x = 55.9 \frac{g}{mol}) in carbon monoxide (co) yields the pure metal and carbon dioxide. the mass of the metal product is 2.83 g. from the data given, use the simplest formula of the oxide to write a balanced equation for the reaction. use x to denote the metal. part: 0 / 2 part 1 of 2 what is the simplest formula of the oxide?

Explanation:

Step1: Calculate the mass of oxygen in the oxide

The mass of the metal oxide is \(m_{oxide}=4.05\space g\) and the mass of the metal is \(m_{metal} = 2.83\space g\).
Using the formula \(m_{O}=m_{oxide}-m_{metal}\), we have \(m_{O}=4.05 - 2.83=1.22\space g\)

Step2: Calculate the moles of metal and oxygen

The molar mass of the metal \(X\) is \(M_X = 55.9\space g/mol\), and the molar mass of oxygen \(M_O=16.0\space g/mol\)
The moles of metal \(n_X=\frac{m_{metal}}{M_X}=\frac{2.83\space g}{55.9\space g/mol}\approx0.0506\space mol\)
The moles of oxygen \(n_O=\frac{m_{O}}{M_O}=\frac{1.22\space g}{16.0\space g/mol}= 0.07625\space mol\)

Step3: Find the mole - ratio

Divide each number of moles by the smaller number of moles (\(n_X = 0.0506\space mol\))
For \(X\): \(\frac{n_X}{n_X}=1\)
For \(O\): \(\frac{n_O}{n_X}=\frac{0.07625}{0.0506}\approx1.5\)
Multiply by \(2\) to get whole - numbers. So the ratio \(X:O = 2:3\)

Answer:

\(X_2O_3\)