Final answer:
To calculate the mole fraction of water vapor in the gas mixture after 58% of the ammonium nitrate decomposes, you need to find the moles of each gas produced and calculate the mole fraction. The mole fraction of water vapor in the gas mixture is 0.404.
Step-by-step explanation:
To calculate the mole fraction of water vapor in the gas mixture after 58% of the ammonium nitrate decomposes, we need to first determine the number of moles of water vapor and nitrogen oxide produced. From the balanced equation:
NH4NO3 (s) → N2O(g) + 2H2O (1)
We can see that for every 1 mole of ammonium nitrate decomposed, we produce 2 moles of water vapor. So, if 58% of the ammonium nitrate decomposes, we would have 0.58 moles of water vapor.
To find the mole fraction of water vapor, we need to compare the moles of water vapor to the total moles of gases produced, which is the sum of the moles of water vapor and nitrogen oxide:
Total moles of gases = moles of water vapor + moles of nitrogen oxide = 0.58 + (0.58/2)
Finally, the mole fraction of water vapor can be calculated by dividing the moles of water vapor by the total moles of gases:
Mole fraction of water vapor = moles of water vapor / total moles of gases
Substituting the values,
Mole fraction of water vapor = 0.58 / (0.58 + (0.58/2)) = 0.404
Therefore, the mole fraction of water vapor in the gas mixture is 0.404.