Question

2 step conversion practice

1. convert 2.5 moles of magnesium into atoms
2. calculate 5.0 moles of sulfur to grams

Explanation:

Question 17: Convert 2.5 moles of magnesium into atoms

Step1: Recall Avogadro's number

Avogadro's number is \( 6.022 \times 10^{23} \) atoms/mol, which relates moles to number of atoms. The formula to convert moles to atoms is: \( \text{Number of atoms} = \text{Moles} \times \text{Avogadro's number} \)

Step2: Substitute the values

We have moles of magnesium = 2.5 mol. Substitute into the formula:
\( \text{Number of atoms} = 2.5 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \)

Step3: Calculate the result

\( 2.5 \times 6.022 \times 10^{23} = 15.055 \times 10^{23} = 1.5055 \times 10^{24} \) atoms (we can round to appropriate significant figures, here 2.5 has two significant figures, so \( 1.5 \times 10^{24} \) or keep more decimals as \( 1.5055 \times 10^{24} \))

Step1: Recall molar mass of sulfur

The molar mass of sulfur (S) is approximately 32.07 g/mol (since sulfur is often considered as S, not \( S_8 \) here for simplicity, or if it's \( S_8 \), molar mass would be \( 8 \times 32.07 = 256.56 \) g/mol, but typically in such problems, if not specified, we use atomic sulfur molar mass 32.07 g/mol). The formula to convert moles to grams is: \( \text{Mass (g)} = \text{Moles} \times \text{Molar Mass (g/mol)} \)

Step2: Substitute the values

Moles of sulfur = 5.0 mol, molar mass of S = 32.07 g/mol.
\( \text{Mass} = 5.0 \, \text{mol} \times 32.07 \, \text{g/mol} \)

Step3: Calculate the result

\( 5.0 \times 32.07 = 160.35 \) g. With two significant figures (from 5.0), it's 160 g (or 1.6 × 10² g)

Answer:

\( \boldsymbol{1.51 \times 10^{24}} \) atoms (or \( 1.5 \times 10^{24} \), depending on significant figures)

Question 18: Calculate 5.0 moles of sulfur to grams