Certainly! Let's break down the calculation process step by step to find out how many grams of acetylene (C2H2) are produced by adding water to 5.00 grams of calcium carbide (CaC2).
Step 1: Determine the molar masses
1. Molar mass of Calcium Carbide (CaC2):
[tex]\[ \text{CaC2} : \text{Calcium (Ca)} = 40.08 \; \text{g/mol} + 2 \times \text{Carbon (C)} = 2 \times 12.01 \; \text{g/mol} \][/tex]
[tex]\[ \text{Molar mass of CaC2} = 40.08 \; \text{g/mol} + 24.02 \; \text{g/mol} = 64.10 \; \text{g/mol} \][/tex]
2. Molar mass of Acetylene (C2H2):
[tex]\[ \text{C2H2} : 2 \times \text{Carbon (C)} = 2 \times 12.01 \; \text{g/mol} + 2 \times \text{Hydrogen (H)} = 2 \times 1.01 \; \text{g/mol} \][/tex]
[tex]\[ \text{Molar mass of C2H2} = 24.02 \; \text{g/mol} + 2.02 \; \text{g/mol} = 26.04 \; \text{g/mol} \][/tex]
Step 2: Calculate the moles of CaC2
Given the mass of CaC2 is 5.00 grams and the molar mass is 64.10 g/mol, we can calculate the number of moles using the formula:
[tex]\[ \text{Moles of CaC2} = \frac{\text{Mass}}{\text{Molar mass}} \][/tex]
[tex]\[ \text{Moles of CaC2} = \frac{5.00 \; \text{g}}{64.10 \; \text{g/mol}} \][/tex]
[tex]\[ \text{Moles of CaC2} \approx 0.0780 \; \text{mol} \][/tex]
Step 3: Determine the moles of C2H2 produced
According to the chemical reaction:
[tex]\[ \text{CaC2} + 2\text{H2O} \rightarrow \text{C2H2} + \text{Ca(OH)2} \][/tex]
1 mole of CaC2 produces 1 mole of C2H2. Therefore, the moles of C2H2 produced are equal to the moles of CaC2 used.
[tex]\[ \text{Moles of C2H2} = 0.0780 \; \text{mol} \][/tex]
Step 4: Calculate the mass of C2H2 produced
Using the moles of C2H2 and its molar mass:
[tex]\[ \text{Mass of C2H2} = \text{Moles of C2H2} \times \text{Molar mass of C2H2} \][/tex]
[tex]\[ \text{Mass of C2H2} = 0.0780 \; \text{mol} \times 26.04 \; \text{g/mol} \][/tex]
[tex]\[ \text{Mass of C2H2} \approx 2.03 \; \text{g} \][/tex]
Therefore, by adding water to 5.00 grams of CaC2, approximately 2.03 grams of acetylene (C2H2) are produced.
