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How many moles of nitrogen gas are needed to react with 7.5 moles of hydrogen?

N2 + 3 H2 to 2 NH3

1 Answer

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SOLUTION:

The balanced chemical equation for the reaction between nitrogen gas (
N_2) and hydrogen gas (
H_2) is:


N_2 + 3H_2 \rightarrow 2NH_3

According to the stoichiometry of the reaction, 1 mole of
N_2 reacts with 3 moles of
H_2 to produce 2 moles of
NH_3.

Therefore, to determine how many moles of
N_2 are needed to react with 7.5 moles of
H_2, we need to use the mole ratio between
N_2 and
H_2:


\rm 1\: mole\: N_2 : 3\: moles\: H_2

We can use this ratio to set up a proportion:


\rm\frac{1\: \text{mol}\: N_2}{3\: \text{mol}\: H_2} = \frac{x\: \text{mol}\: N_2}{7.5\ \text{mol}\: H_2}

Solving for x, we get:


\rm{x = \frac{1\: \text{mol}\: N_2}{3\: \text{mol}\: H_2} \cdot 7.5\: \text{mol}\: H_2 = \boxed{2.5}\: \text{mol}\: N_2}


\therefore 2.5 moles of
N_2 are needed to react with 7.5 moles of
H_2.


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