Part 1:
Using the balanced equation, we see that the ratio of moles of C2H2 to moles of O2 is 2:3. Therefore, if 6.0 mol of C2H2 is used, the moles of O2 needed would be:
6.0 mol C2H2 x (3 mol O2 / 2 mol C2H2) = 9.0 mol O2
So, 9.0 mol of O2 are needed to react completely with 6.0 mol of C2H2.
Part 2:
Using the balanced equation, we see that the ratio of moles of C2H2 to moles of H2O is 2:2. Therefore, if 0.59 mol of H2O is formed, the moles of C2H2 needed would be:
0.59 mol H2O x (2 mol C2H2 / 2 mol H2O) = 0.59 mol C2H2
So, 0.59 mol of C2H2 are needed to form 0.59 mol of H2O.
Part 3:
Using the balanced equation, we see that the ratio of moles of C2H2 to moles of CO is 2:4. Therefore, if 0.82 mol of CO is formed, the moles of C2H2 needed would be:
0.82 mol CO x (2 mol C2H2 / 4 mol CO) = 0.41 mol C2H2
So, 0.41 mol of C2H2 are needed to form 0.82 mol of CO.