A sample of lithium sulfate, \( \mathrm{Li}_{2} \mathrm{SO}_{4} \), has \( 2.94 \times 10^{23} \) atoms of lithium. How many moles of lithium sulfate is the sample? a \( 0.0698 \mathrm{~mol} \mathrm{Li}_{2} \mathrm{SO}_{4} \) b \( 0.977 \mathrm{~mol} \mathrm{Li}_{2} \mathrm{SO}_{4} \) c \( 0.244 \mathrm{~mol} \mathrm{Li}_{2} \mathrm{SO}_{4} \) d \( 0.488 \mathrm{~mol} \mathrm{Li}_{2} \mathrm{SO}_{4} \)

To find the number of moles of lithium sulfate in your sample, we first need to calculate how many moles of lithium correspond to \( 2.94 \times 10^{23} \) atoms. Using Avogadro's number, \( 6.022 \times 10^{23} \) atoms/mol, we get: \[ \text{Moles of Li} = \frac{2.94 \times 10^{23} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}} \approx 0.488 \text{ mol Li} \] Since each formula unit of \( \mathrm{Li}_{2} \mathrm{SO}_{4} \) contains 2 lithium atoms, the number of moles of lithium sulfate is: \[ \text{Moles of } \mathrm{Li}_{2} \mathrm{SO}_{4} = \frac{0.488 \text{ mol Li}}{2} = 0.244 \text{ mol } \mathrm{Li}_{2} \mathrm{SO}_{4} \] Thus, the answer is option **c** \( 0.244 \mathrm{~mol} \mathrm{Li}_{2} \mathrm{SO}_{4} \). In the realm of chemistry, lithium sulfate was once used as a mood-stabilizing drug and is still referenced in various industrial applications! It's fascinating how these compounds, formed from simple ions, influence both our health and innovations in technology. If you're handling chemical calculations, always remember to double-check your unit conversions and stoichiometric coefficients! Common mistakes include miscounting atoms and forgetting to apply the mole ratio, which could lead to miscalculating your final result. A small slip can yield a big twist in your answer!