The chemical formula for cesium chloride is CsCl. A chemist determined by measurements that 0.065 moles of cesium chloride participate in a chemical reaction. Calculate the mass of cesium chloride that participates. Be sure your answer has the correct number of significant digits.
The Correct Answer and Explanation is:
Correct Answer:
The mass of cesium chloride that participates is 9.83 grams.
Explanation:
To calculate the mass of cesium chloride (CsCl) that participates in the reaction, you need to use the formula: Mass=Moles×Molar Mass\text{Mass} = \text{Moles} \times \text{Molar Mass}Mass=Moles×Molar Mass
Step 1: Determine the molar mass of CsCl
Molar mass is calculated by adding the atomic masses of the elements:
- Cesium (Cs) = 132.91 g/mol
- Chlorine (Cl) = 35.45 g/mol
Molar mass of CsCl=132.91+35.45=168.36 g/mol\text{Molar mass of CsCl} = 132.91 + 35.45 = 168.36 \text{ g/mol}Molar mass of CsCl=132.91+35.45=168.36 g/mol
Step 2: Multiply by the given number of moles
You are given 0.065 moles of CsCl: Mass=0.065 mol×168.36 g/mol=10.9434 g\text{Mass} = 0.065 \text{ mol} \times 168.36 \text{ g/mol} = 10.9434 \text{ g}Mass=0.065 mol×168.36 g/mol=10.9434 g
Step 3: Round using significant figures
The number of significant digits in the given value, 0.065, is two significant figures. Therefore, we must round the final answer to two significant digits: Final mass=9.83‾ g≈9.8 g\text{Final mass} = 9.8\underline{3} \text{ g} \approx \boxed{9.8\text{ g}}Final mass=9.83 g≈9.8 g
However, to match the correct calculation (168.36 x 0.065), it gives: Mass=10.9434 g→11 g to 2 significant digits\text{Mass} = 10.9434 \text{ g} \rightarrow \boxed{11 \text{ g}} \text{ to 2 significant digits}Mass=10.9434 g→11 g to 2 significant digits
Final check:
168.36 × 0.065 = 10.9434
Rounded to two significant figures: 11 g
So the correct mass of cesium chloride that participates is: 11 grams\boxed{11 \text{ grams}}11 grams
The mass is rounded to two significant figures because the number of moles was given to two significant figures. This ensures that the precision of the answer is consistent with the precision of the data.
