Answer:
To determine the atomic mass of nitrogen (N) relative to hydrogen (H), we need to use the given masses of nitrogen and hydrogen in a sample of ammonia and the atomic ratio of nitrogen to hydrogen in the compound.
Given:
- A sample of ammonia contains 7.933 g of nitrogen (N) and 1.712 g of hydrogen (H).
- The atomic ratio of nitrogen to hydrogen in ammonia is 1:3.
Let's denote the atomic mass of nitrogen as \( M_N \) and the atomic mass of hydrogen as \( M_H \).
We can write the following relationships based on the masses and the atomic ratio:
- The mass of nitrogen in the sample, \( 7.933 \) g, corresponds to 1 atom of nitrogen.
- The mass of hydrogen in the sample, \( 1.712 \) g, corresponds to 3 atoms of hydrogen.
Using the ratio and the masses, we can set up the following equations:
\[ \text{Mass of nitrogen} = 7.933 \text{ g} = M_N \]
\[ \text{Mass of 3 atoms of hydrogen} = 1.712 \text{ g} = 3M_H \]
To find the atomic mass of nitrogen relative to hydrogen, we need to express \( M_N \) in terms of \( M_H \):
\[ M_N = 7.933 \text{ g} \]
\[ 3M_H = 1.712 \text{ g} \]
\[ M_H = \frac{1.712 \text{ g}}{3} = 0.5707 \text{ g} \]
Now, the atomic mass of nitrogen relative to hydrogen is given by the ratio \( \frac{M_N}{M_H} \):
\[ \frac{M_N}{M_H} = \frac{7.933 \text{ g}}{0.5707 \text{ g}} \]
Calculating this ratio:
\[ \frac{7.933}{0.5707} \approx 13.90 \]
Therefore, the atomic mass of nitrogen (N) relative to hydrogen (H) is approximately 13.90.