To determine the mass of calcium carbide (CaC2) required to produce a specific volume of acetylene (C2H2) according to the equation CaC2 + 2 H2O → C2H2 + Ca(OH)2, we need to use stoichiometry and the molar ratios between the reactants and products.
The molar ratio between CaC2 and C2H2 in the balanced equation is 1:1. This means that 1 mole of CaC2 will produce 1 mole of C2H2.
First, we need to convert the given volume of acetylene (100 cm³) to moles. To do this, we use the ideal gas law, assuming standard temperature and pressure:
PV = nRT
Assuming standard temperature (273 K) and pressure (1 atm), the ideal gas constant (R) is 0.0821 L·atm/(mol·K). Converting the volume to liters:
V = 100 cm³ = 0.1 L
Now, we can calculate the number of moles of C2H2:
n = PV / RT = (1 atm × 0.1 L) / (0.0821 L·atm/(mol·K) × 273 K) ≈ 0.004 mol
Since the molar ratio between CaC2 and C2H2 is 1:1, we know that 0.004 mol of CaC2 is required to produce 0.004 mol of C2H2.
Finally, we can calculate the mass of CaC2 using its molar mass. The molar mass of CaC2 is the sum of the atomic masses of calcium (Ca) and carbon (C) multiplied by 2 for the two carbon atoms:
Molar mass of CaC2 = (40.08 g/mol + 12.01 g/mol) × 2 = 64.18 g/mol
Mass of CaC2 = number of moles × molar mass = 0.004 mol × 64.18 g/mol ≈ 0.26 g
Therefore, approximately 0.26 grams of calcium carbide (CaC2) would be needed to produce 100 cm³ of acetylene (C2H2) according to the given equation.