Consider the following balanced equation.

2N2H4(g)+N2O4(g)→3N2(g)+4H2O(g) Complete the following table, showing the appropriate number of moles of reactants and products. If the number of moles of a reactant is provided, fill in the required amount of the other reactant, as well as the moles of each product formed. If the number of moles of a product is provided, fill in the required amount of each reactant to make that amount of product, as well as the amount of the other product that is made.
molN2H4 molN2O4 molN2 molH2O
_____ 1 _____ _____
2 _____ _____ _____
_____ _____ _____ 8
_____ 1.9 _____ _____
1.0 _____ _____ _____
_____ _____ 37.8 _____

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molN2H4 molN2O4 molN2 molH2O

_____ 1 3 4
2 1 3 4
3 6 9 12
_____ 1.9 5.7 7.6
1.0 0.5 1.5 2.0
_____ _____ 37.8 50.4

To complete the table, we need to use the stoichiometry of the balanced equation to determine the appropriate number of moles of reactants and products.

Let's go step by step:

1. ____ mol N2H4 1 mol N2O4 _____ mol N2 _____ mol H2O
In this case, the number of moles of N2O4 is given (1 mol). From the balanced equation, we can see that the stoichiometric ratio between N2O4 and N2H4 is 1:2. So, we can calculate the moles of N2H4 as follows:
2 moles N2H4 = 1 mole N2O4
Therefore, the moles of N2H4 would be 2 * 1 = 2 mol.
Now, to find the moles of N2 and H2O produced, we can use the stoichiometric ratios again:
2 moles N2H4 produce 3 moles N2
2 moles N2H4 produce 4 moles H2O
Therefore, the moles of N2 and H2O would be 2 * 3 = 6 mol and 2 * 4 = 8 mol, respectively.

2. 2 mol N2H4 _____ mol N2 _____ mol H2O
In this case, the number of moles of N2H4 is given (2 mol). From the balanced equation, we can see that the stoichiometric ratio between N2H4 and N2 is 2:3, and between N2H4 and H2O is 2:4.
So, we can calculate the moles of N2 and H2O as follows:
2 moles N2H4 produce 3 moles N2
2 moles N2H4 produce 4 moles H2O
Therefore, the moles of N2 and H2O would be 2 * 3 = 6 mol and 2 * 4 = 8 mol, respectively.

3. ____ mol N2H4 ____ mol N2 ____ mol H2O 8 mol
In this case, the number of moles of H2O is given (8 mol). From the balanced equation, we can see that the stoichiometric ratio between H2O and N2H4 is 4:2. So, we can calculate the moles of N2H4 as follows:
4 moles H2O = 2 moles N2H4
Therefore, the moles of N2H4 would be 2 * 8/4 = 4 mol.
Now, to find the moles of N2, we can use the stoichiometric ratio:
2 moles N2H4 produce 3 moles N2
Therefore, the moles of N2 would be 2 * 3/2 * 8/4 = 6 mol.

4. ____ mol N2H4 1.9 mol N2O4 _____ mol N2 _____ mol H2O
In this case, the number of moles of N2O4 is given (1.9 mol). From the balanced equation, we can see that the stoichiometric ratio between N2O4 and N2H4 is 1:2. So, we can calculate the moles of N2H4 as follows:
2 moles N2H4 = 1 mole N2O4
Therefore, the moles of N2H4 would be 2 * 1.9 = 3.8 mol.
Now, to find the moles of N2 and H2O produced, we can use the stoichiometric ratios again:
2 moles N2H4 produce 3 moles N2
2 moles N2H4 produce 4 moles H2O
Therefore, the moles of N2 and H2O would be 2 * 3.8 * 3/2 = 11.4 mol and 2 * 3.8 * 4/2 = 15.2 mol, respectively.

5. 1.0 mol N2H4 _____ mol N2 _____ mol H2O
In this case, the number of moles of N2H4 is given (1.0 mol). From the balanced equation, we can see that the stoichiometric ratio between N2H4 and N2 is 2:3, and between N2H4 and H2O is 2:4.
So, we can calculate the moles of N2 and H2O as follows:
2 moles N2H4 produce 3 moles N2
2 moles N2H4 produce 4 moles H2O
Therefore, the moles of N2 and H2O would be 2 * 3/2 * 1.0 = 3 mol and 2 * 4/2 * 1.0 = 4 mol, respectively.

6. ____ mol N2H4 ____ mol N2 37.8 mol _____ mol H2O
In this case, the number of moles of N2 is given (37.8 mol). From the balanced equation, we can see that the stoichiometric ratio between N2 and N2H4 is 3:2. So, we can calculate the moles of N2H4 as follows:
3 moles N2 = 2 moles N2H4
Therefore, the moles of N2H4 would be 2 * 37.8/3 = 25.2 mol.
Now, to find the moles of H2O, we can use the stoichiometric ratio:
2 moles N2H4 produce 4 moles H2O
Therefore, the moles of H2O would be 4 * 37.8/3 = 50.4 mol.

I hope this helps you complete the table! Remember to always use the stoichiometric ratios from the balanced equation to find the appropriate number of moles for reactants and products.