QuestionHow many moles of $\mathrm{N}_{2}$ are needed to react with 4 moles of $\mathrm{H}_{2}$ in the equation $3 \mathrm{H}_{2}+\mathrm{N}_{2} \rightarrow 2 \mathrm{NH}_{3}$ ? A) 1.0 B) 1.1 C) 4.0 D) 1.3 E) 2.5

Studdy Solution

STEP 1

Assumptions1. The given reaction is $3 \mathrm{H}_{}+\mathrm{}_{} \rightarrow \mathrm{NH}_{3}$ . We are given that4 moles of $\mathrm{H}_{}$ are present3. We assume that the reaction goes to completion, meaning all of the $\mathrm{H}_{}$ reacts4. We are asked to find the number of moles of $\mathrm{}_{}$ required

STEP 2

The stoichiometry of the reaction tells us the ratio of moles of reactants and products. From the balanced chemical equation, we can see that moles of $\mathrm{H}_{2}$ react with1 mole of $\mathrm{}_{2}$ .

STEP 3

We can set up a proportion to find the number of moles of $\mathrm{}_{2}$ required $\frac{3 \, \text{moles of} \, \mathrm{H}_{2}}{1 \, \text{mole of} \, \mathrm{}_{2}} = \frac{ \, \text{moles of} \, \mathrm{H}_{2}}{x \, \text{moles of} \, \mathrm{}_{2}}$

STEP 4

We can now solve for $x$ , the number of moles of $\mathrm{}_{2}$ required. Cross-multiplying gives $3x =4$

STEP 5

Finally, we solve for $x$ by dividing both sides of the equation by3 $x = \frac{4}{3}$ So,1.33 moles of $\mathrm{}_{2}$ are required to react with4 moles of $\mathrm{H}_{2}$ .Looking at the given options, the closest one is1.3, so the answer is D)1.3.

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