Answer
a. To calculate the number of moles in 27.0 g calcium, the conversion factor should be : 1 mole Ca / Molar mass Ca
b. The correct conversion factor should be : $\frac{{2 mol} (K^{+} ions)}{{1mol_(K_{2}SO_{4})}}$
c. The correct conversion factor should be: $\frac{2 mole (H_{2}O)}{2 mol (Na)}$
Work Step by Step
a. The mistake is in the conversion factor that she is using ( 1 mole/ Avogadro's number).
To calculate the number of moles in 27.0 g calcium, the conversion factor should be : 1 mole Ca / Molar mass Ca:
27.01 g Ca x $\frac{1 mol (Ca) }{40.0 g}$ = 0.675 mol Ca. ( or 0.68 mole Ca to three significant figures).
b. The mistake is in the conversion factor that she is using. Based on the chemical formula, there are 2 mol of $K^{+}$ ions in 1 mole $K_{2}SO_{4}$.
So the correct answer on the number of $K^{+}$ in 2.5 mole $K_{2}SO_{4}$should be :
2.5 mole $K_{2}SO_{4}$ x $\frac{{2 mole} (K^{+} ions)}{{1mole_(K_{2}SO_{4})}}$ = 5 $mole (K^{+} ions)$
So there are 5 $mole (K^{+} ions)$ in 2.5 mole $K_{2}SO_{4}$ .
c. The mistake is in the conversion factor that she is using.
Based on the balanced equation of the chemical reaction, 2 moles Na enter in reaction with 2 moles water.
So the correct answer on the number of moles water that react withh 0.50 moles of Na:
0.50 mole Na x $\frac{2 mole (H_{2}O)}{2 mol (Na)}$ = 0.50 mol water.
So 0.5 mol water are required to react with 0.50 mol Na.
