If 10.5 g of hydrogen, H2, were mixed with 6.51 g of acetylene, C2H2, and allowed to react according to the following equation, what is the theoretical yield of ethane,C2H6 produced.
To determine the theoretical yield of ethane (C2H6) produced, we first need to balance the chemical equation for the reaction between hydrogen (H2) and acetylene (C2H2).
The balanced equation is:
2 H2 + C2H2 → C2H6
From the balanced equation, we can see that for every 2 moles of hydrogen (H2) and 1 mole of acetylene (C2H2), we can produce 1 mole of ethane (C2H6).
Now, let's calculate the number of moles of hydrogen (H2) and acetylene (C2H2) we have.
The molar mass of hydrogen (H2) is 2.016 g/mol. Therefore, the number of moles of hydrogen is calculated as:
n(H2) = mass(H2) / molar mass(H2)
n(H2) = 10.5 g / 2.016 g/mol ≈ 5.2 mol
The molar mass of acetylene (C2H2) is 26.04 g/mol. Therefore, the number of moles of acetylene is calculated as:
n(C2H2) = mass(C2H2) / molar mass(C2H2)
n(C2H2) = 6.51 g / 26.04 g/mol ≈ 0.25 mol
Now, we compare the number of moles of reactants to determine the limiting reactant. The limiting reactant is the one that is fully consumed in the reaction and determines the maximum amount of product that can be produced.
Looking at the balanced equation, we can see that 2 moles of hydrogen (H2) are required for each mole of acetylene (C2H2). Since we have more than twice the number of moles of hydrogen than acetylene, hydrogen is in excess. Therefore, acetylene is the limiting reactant.
Now, let's calculate the number of moles of ethane (C2H6) that can be produced using the limiting reactant, acetylene (C2H2).
According to the balanced equation, the molar ratio between acetylene (C2H2) and ethane (C2H6) is 1:1. So, the number of moles of ethane formed is also 0.25 mol.
Finally, to find the theoretical yield of ethane (C2H6) in grams, we use the molar mass of ethane, which is 30.07 g/mol.
The theoretical yield of ethane (C2H6) can be calculated as:
mass(C2H6) = n(C2H6) × molar mass(C2H6)
mass(C2H6) = 0.25 mol × 30.07 g/mol ≈ 7.52 g
Therefore, the theoretical yield of ethane (C2H6) produced is approximately 7.52 grams.