Calculate the percentage by mass of nitrogen in calcium trioxonitrate (V) [Ca = 40, N = 14, O = 16]

1. Analyze the question

We need to find the percentage by mass of nitrogen in calcium trioxonitrate(V).

• Chemical Formula: Calcium is $Ca^{2+}$ and trioxonitrate(V) is $NO_3^-$. Therefore, the formula is $Ca(NO_3)_2$.
• Given Atomic Masses: $Ca = 40$, $N = 14$, $O = 16$.

2. Explain the concept

The percentage by mass of an element in a compound is calculated using the formula:

3. Show the solution

Step 1: Calculate the molar mass of $Ca(NO_3)_2$

• $Ca = 1 \times 40 = 40$
• $N = 2 \times 14 = 28$ (Note: there are two nitrogen atoms because of the subscript 2 outside the bracket)
• $O = 6 \times 16 = 96$ (Note: $3 \times 2 = 6$ oxygen atoms)

Total Molar Mass = $40 + 28 + 96 = 164 \text{ g/mol}$

Step 2: Calculate the total mass of Nitrogen

• Mass of Nitrogen = $2 \times 14 = 28 \text{ g/mol}$

Step 3: Calculate the percentage

4. Identify the answer

Comparing our result to the options provided, the correct option is C.

5. Exam Tip

Always pay close attention to the subscripts in brackets! Many students forget to multiply the atoms inside the bracket (like $NO_3$) by the subscript outside (the 2 in $Ca(NO_3)_2$). If you had calculated for $CaNO_3$ instead, you would have gotten the wrong answer. Always write out the full formula clearly before starting your calculation.