if a reaction vessel contains 11.5g NH3, 12.0g O2, and 10.5g CH4, what is the maximum mass in grams of hydrogen cyanide that could be made?
To find the maximum mass of hydrogen cyanide (HCN) that could be produced, we need to determine the limiting reactant. The limiting reactant is the reactant that is completely consumed first and determines the maximum amount of product that can be formed.
To identify the limiting reactant, we compare the given amounts of each reactant with their respective molar masses. The balanced chemical equation for the reaction between NH3 (ammonia), O2 (oxygen), and CH4 (methane) to form HCN (hydrogen cyanide) is:
4NH3 + 5O2 + CH4 → 2HCN + 6H2O
First, we need to convert the given masses of NH3, O2, and CH4 into moles. To do this, divide the mass of each compound by its molar mass:
Molar mass of NH3 (ammonia) = 14.01 g/mol + 3(1.01 g/mol) = 17.03 g/mol
Moles of NH3 = 11.5 g NH3 / 17.03 g/mol = 0.675 mol NH3
Molar mass of O2 (oxygen) = 2(16.00 g/mol) = 32.00 g/mol
Moles of O2 = 12.0 g O2 / 32.00 g/mol = 0.375 mol O2
Molar mass of CH4 (methane) = 12.01 g/mol + 4(1.01 g/mol) = 16.05 g/mol
Moles of CH4 = 10.5 g CH4 / 16.05 g/mol = 0.653 mol CH4
Now, we compare the moles of each reactant to the stoichiometric coefficients in the balanced equation to determine which reactant is limiting.
The stoichiometric ratio between NH3 and HCN is 4:2, which means that 4 moles of NH3 react to form 2 moles of HCN. Therefore, the maximum moles of HCN that can be formed from NH3 is 0.675 mol NH3 * (2 mol HCN / 4 mol NH3) = 0.3375 mol HCN
The stoichiometric ratio between O2 and HCN is 5:2, which means that 5 moles of O2 react to form 2 moles of HCN. Therefore, the maximum moles of HCN that can be formed from O2 is 0.375 mol O2 * (2 mol HCN / 5 mol O2) = 0.15 mol HCN
The stoichiometric ratio between CH4 and HCN is 1:2, which means that 1 mole of CH4 reacts to form 2 moles of HCN. Therefore, the maximum moles of HCN that can be formed from CH4 is 0.653 mol CH4 * (2 mol HCN / 1 mol CH4) = 1.306 mol HCN
Based on the calculations, we can see that the moles of HCN that can be produced from NH3 (0.3375 mol HCN) and O2 (0.15 mol HCN) are both lower than the moles of HCN that can be produced from CH4 (1.306 mol HCN). Therefore, the limiting reactant is O2.
Now, we need to calculate the mass of HCN produced using the limiting reactant.
Molar mass of HCN (hydrogen cyanide) = 1.01 g/mol + 12.01 g/mol + 14.01 g/mol = 27.03 g/mol
Moles of HCN produced = 0.15 mol HCN (from O2 as the limiting reactant)
Mass of HCN produced = Moles of HCN produced * Molar mass of HCN
= 0.15 mol HCN * 27.03 g/mol
= 4.0545 g
Therefore, the maximum mass of hydrogen cyanide (HCN) that could be produced is 4.0545 grams.