N2 + 3 H2 → 2 NH3

To calculate the number of hydrogen molecules needed, we need to determine the number of moles of ammonia produced and then use the stoichiometry of the reaction to calculate the number of moles of hydrogen required.

Step 1: Calculate the number of moles of ammonia produced

The molar mass of ammonia (NH3) is 17.04 g/mol. Therefore, the number of moles of ammonia produced is:

$$\text{Moles of NH}_3$$=\frac{\text{Mass of NH}_3}{\text{Molar mass of NH}_3}$$

$$=\frac{525 \text{ g}}{17.04 \text{ g/mol}}$$

$$=30.78 \text{ mol}$$

Step 2: Calculate the number of moles of hydrogen required

According to the balanced chemical equation, 3 moles of hydrogen (H2) are required to produce 2 moles of ammonia. Therefore, the number of moles of hydrogen required is:

$$\text{Moles of H}_2$$=\frac{3\text{ mol H}_2}{2\text{ mol NH}_3}\times \text{Moles of NH}_3$$

$$=\frac{3\text{ mol H}_2}{2\text{ mol NH}_3}\times 30.78 \text{ mol}$$

$$=46.17 \text{ mol}$$

Step 3: Calculate the number of hydrogen molecules

Since 1 mole of any gas contains $$6.022\times10^{23} \text{ molecules }$$, the number of hydrogen molecules required is:

Number of H2 molecules =$$ \text{Moles of H}_2\times\text{ Avogadro's Number}$$

$$=46.17\text{ mol} \times 6.022\times10^{23} \text{ molecules/mol}$$

$$=2.78 \times 10^{25} \text{ molecules}$$

Therefore, 2.78 x 10^25 hydrogen molecules are required to produce 525 grams of ammonia.