what is the mass in grams of a sample of $v_2o_3$ that contains $1.03\times10^{12}$ atoms of o?

Explanation:

Step1: Calculate the number of moles of (O) atoms

Use Avogadro's number (N_A = 6.022\times 10^{23}\text{ atoms/mol}). The number of moles of (O) atoms, (n_O=\frac{1.03\times 10^{12}\text{ atoms}}{6.022\times 10^{23}\text{ atoms/mol}}) [n_O=\frac{1.03}{6.022}\times10^{- 11}\text{ mol}\approx1.71\times 10^{-12}\text{ mol}]

Step2: Relate moles of (O) to moles of (V_2O_3)

From the formula (V_2O_3), the ratio of (n_{V_2O_3}:n_O = 1:3). So (n_{V_2O_3}=\frac{n_O}{3}) [n_{V_2O_3}=\frac{1.71\times 10^{-12}\text{ mol}}{3}=5.7\times 10^{-13}\text{ mol}]

Step3: Calculate the molar mass of (V_2O_3)

The molar mass of (V) is (M_V = 50.94\text{ g/mol}) and of (O) is (M_O=16.00\text{ g/mol}). (M_{V_2O_3}=2\times50.94 + 3\times16.00=101.88+48.00 = 149.88\text{ g/mol})

Step4: Calculate the mass of (V_2O_3)

Use the formula (m = n\times M). (m_{V_2O_3}=n_{V_2O_3}\times M_{V_2O_3}) [m_{V_2O_3}=5.7\times 10^{-13}\text{ mol}\times149.88\text{ g/mol}\approx8.54\times 10^{-11}\text{ g}]

Answer:

(8.54\times 10^{-11}\text{ g})