Answered

The Haber process can be used to produce ammonia [tex] \left( NH_3 \right) [/tex] from hydrogen gas [tex] \left( H_2 \right) [/tex] and nitrogen gas [tex] \left( N_2 \right) [/tex]. The balanced equation for this process is shown below.

[tex]\[ 3 H_2 + N_2 \rightarrow 2 NH_3 \][/tex]

The molar mass of [tex] NH_3 [/tex] is [tex] 17.03 \, g/mol [/tex]. The molar mass of [tex] H_2 [/tex] is [tex] 2.0158 \, g/mol [/tex]. In a particular reaction, [tex] 0.575 \, g [/tex] of [tex] NH_3 [/tex] forms. What is the mass, in grams, of [tex] H_2 [/tex] that must have reacted, to the correct number of significant figures?

A. 0.1 grams
B. 0.102 grams
C. 0.10209 grams
D. 0.1021 grams



Answer :

GinnyAnswer
To determine the mass of \( \text{H}_2 \) that must have reacted to form \( 0.575 \) grams of \( \text{NH}_3 \), we will follow a step-by-step approach.

1. Calculate the moles of \( \text{NH}_3 \) formed:

We start by using the molar mass of \( \text{NH}_3 \):
[tex]\[ \text{Molar mass of } \text{NH}_3 = 17.03 \text{ g/mol} \][/tex]

Using the given mass of \( \text{NH}_3 \):
[tex]\[ \text{Mass of } \text{NH}_3 \text{ formed} = 0.575 \text{ g} \][/tex]

We calculate the moles of \( \text{NH}_3 \) as follows:
[tex]\[ \text{Moles of } \text{NH}_3 = \frac{\text{Mass of } \text{NH}_3}{\text{Molar mass of } \text{NH}_3} = \frac{0.575 \text{ g}}{17.03 \text{ g/mol}} \approx 0.0338 \text{ mol} \][/tex]

2. Use stoichiometry to find the moles of \( \text{H}_2 \) needed:

From the balanced chemical equation:
[tex]\[ 3 \text{ H}_2 + \text{ N}_2 \rightarrow 2 \text{ NH}_3 \][/tex]

This tells us that 3 moles of \( \text{H}_2 \) produce 2 moles of \( \text{NH}_3 \).

Thus, the number of moles of \( \text{H}_2 \) needed can be found using the ratio:
[tex]\[ \text{Moles of } \text{H}_2 = \left( \frac{3}{2} \right) \times \text{Moles of } \text{NH}_3 = \left( \frac{3}{2} \right) \times 0.0338 \text{ mol} \approx 0.0506 \text{ mol} \][/tex]

3. Calculate the mass of \( \text{H}_2 \) needed:

Using the molar mass of \( \text{H}_2 \):
[tex]\[ \text{Molar mass of } \text{H}_2 = 2.0158 \text{ g/mol} \][/tex]

We can now find the mass of \( \text{H}_2 \) needed:
[tex]\[ \text{Mass of } \text{H}_2 = \text{Moles of } \text{H}_2 \times \text{Molar mass of } \text{H}_2 = 0.0506 \text{ mol} \times 2.0158 \text{ g/mol} \approx 0.102 \text{ g} \][/tex]

4. Determine the mass of \( \text{H}_2 \) to the correct number of significant figures:

Given the values provided and the calculation, the mass of \( \text{H}_2 \) to three significant figures would be:

[tex]\[ \boxed{0.102 \text{ grams}} \][/tex]

Thus, the mass of [tex]\( \text{H}_2 \)[/tex] that must have reacted is [tex]\( 0.102 \)[/tex] grams.

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