Final answer:
To produce 100 grams of copper(1) acetylide monohydrate, approximately 0.0116 liters of acetylene gas are required at 770 torr and 25°C, assuming an 85% yield.
Step-by-step explanation:
To determine the volume of acetylene gas required to produce 100 grams of copper(1) acetylide monohydrate, we need to use stoichiometry to calculate the moles of acetylene gas, and then convert that to volume using the ideal gas law. First, we convert the mass of copper(1) acetylide monohydrate to moles using its molar mass. Since the yield is given as 85%, we multiply the calculated moles by 0.85 to get the actual moles of acetylene gas. Next, we use the ideal gas law (PV = nRT) to calculate the volume of acetylene gas in liters.
Given:
- Pressure (P) = 770 torr
- Temperature (T) = 25°C = 298 K
We also need to determine the number of moles of acetylene gas produced when 1 mole of copper(1) acetylide monohydrate is formed. From the balanced chemical equation, we see that 1 mole of copper(1) acetylide monohydrate is produced when 1 mole of acetylene gas is consumed.
Using the molar mass of copper(1) acetylide monohydrate (Cu₂C2H2O), which is approximately 199.06 g/mol, we can calculate the moles of copper(1) acetylide monohydrate produced:
moles = mass / molar mass
moles = 100 g / 199.06 g/mol
moles = 0.502 mol
Since the yield is given as 85%:
actual moles = 0.502 mol * 0.85
actual moles = 0.4267 mol
Now, we can use the ideal gas law to calculate the volume of acetylene gas:
V = (n * R * T) / P
V = (0.4267 mol * 0.0821 L·atm/mol·K * 298 K) / (770 torr / 760 torr/1 atm)
V = 0.0116 L
Therefore, approximately 0.0116 liters of acetylene gas at 770 torr and 25°C are required to produce 100.0 grams of copper(1) acetylide monohydrate, assuming an 85% yield.