Question

what mass, in grams, of calcium chloride dihydrate would she need to use to generate the 1.000 kg of caso₄? molar mass caso₄ = 136.14 g/mol molar mass cacl₂·2h₂o = 147.01 g/mol znso₄·7h₂o + cacl₂·2h₂o → caso₄(s) + zncl₂ + 9h₂o ? g cacl₂·2h₂o

Explanation:

Step1: Convert mass of CaSO₄ to moles

First, convert the mass of \( \text{CaSO}_4 \) from kilograms to grams: \( 1.000 \, \text{kg} = 1000 \, \text{g} \).
Then, use the molar mass of \( \text{CaSO}_4 \) to find moles:
\( \text{Moles of } \text{CaSO}_4 = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{1000 \, \text{g}}{136.14 \, \frac{\text{g}}{\text{mol}}} \approx 7.345 \, \text{mol} \).

Step2: Determine moles of \( \text{CaCl}_2 \cdot 2\text{H}_2\text{O} \)

From the balanced equation, the mole ratio of \( \text{CaCl}_2 \cdot 2\text{H}_2\text{O} \) to \( \text{CaSO}_4 \) is \( 1:1 \). Thus, moles of \( \text{CaCl}_2 \cdot 2\text{H}_2\text{O} = 7.345 \, \text{mol} \).

Step3: Calculate mass of \( \text{CaCl}_2 \cdot 2\text{H}_2\text{O} \)

Use the molar mass of \( \text{CaCl}_2 \cdot 2\text{H}_2\text{O} \) to find mass:
\( \text{Mass} = \text{Moles} \times \text{Molar Mass} = 7.345 \, \text{mol} \times 147.01 \, \frac{\text{g}}{\text{mol}} \approx 1079 \, \text{g} \).

Answer:

\( \boldsymbol{1079} \) (or more precisely, ~1079 g)