Question

calculate the number of vanadium atoms in a 140.0 g sample of vanadium(v) oxide (v₂o₅). be sure your answer has a unit symbol if necessary, and round it to 4 significant digits.

Explanation:

Step1: Calculate molar mass of \(V_2O_5\)

The molar mass of \(V\) is approximately \(50.94\ g/mol\) and of \(O\) is approximately \(16.00\ g/mol\). For \(V_2O_5\), \(M = 2\times50.94+5\times16.00=101.88 + 80.00=181.88\ g/mol\).

Step2: Calculate moles of \(V_2O_5\)

Use the formula \(n=\frac{m}{M}\), where \(m = 140.0\ g\) and \(M = 181.88\ g/mol\). So \(n=\frac{140.0}{181.88}\approx0.7697\ mol\).

Step3: Determine moles of \(V\) atoms

In one - mole of \(V_2O_5\), there are 2 moles of \(V\) atoms. So the number of moles of \(V\) atoms in \(0.7697\ mol\) of \(V_2O_5\) is \(n_V=2\times0.7697 = 1.5394\ mol\).

Step4: Calculate number of \(V\) atoms

Use Avogadro's number \(N_A = 6.022\times10^{23}\ atoms/mol\). The number of \(V\) atoms \(N=n_V\times N_A=1.5394\times6.022\times10^{23}\approx9.270\times 10^{23}\) atoms.

Answer:

\(9.270\times 10^{23}\) atoms