Garza Mcdonald
03/16/2024 · Elementary School
Finding chemical formulae from a mole ratio An unknown compound has the following chemical formula: where \( x \) stands for a whole number. Measurements also show that a certain sample of the unknown compound contains 5.4 mol of nitrogen and 10.84 mol of oxygen. Write the complete chemical formula for the unknown compound.
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Step-by-step Solution
To determine the complete chemical formula for the unknown compound, we need to find the mole ratio of nitrogen (N) to oxygen (O) in the sample.
Given:
- Moles of nitrogen (N) = 5.4 mol
- Moles of oxygen (O) = 10.84 mol
Next, we can find the ratio of nitrogen to oxygen by dividing both values by the smaller number of moles, which is 5.4 mol:
1. Calculate the ratio for nitrogen:
\[
\text{Ratio of N} = \frac{5.4 \, \text{mol}}{5.4 \, \text{mol}} = 1
\]
2. Calculate the ratio for oxygen:
\[
\text{Ratio of O} = \frac{10.84 \, \text{mol}}{5.4 \, \text{mol}} \approx 2.009
\]
Since we are looking for whole number ratios, we can round 2.009 to the nearest whole number, which is 2.
Thus, the mole ratio of nitrogen to oxygen is approximately 1:2.
This means the chemical formula for the unknown compound can be written as:
\[
\text{N}_1\text{O}_2 \quad \text{or simply} \quad \text{NO}_2
\]
Therefore, the complete chemical formula for the unknown compound is:
\[
\text{NO}_2
\]
Quick Answer
The chemical formula for the unknown compound is NO₂.
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