Question

how many moles of gas were added to a balloon that started with 2.3 moles of gas and a volume of 1.4 l given that the final volume was 7.2 l?
○ 12
○ 0.085
○ 9.5
○ 4.4
○ none of the above

Explanation:

Step1: Apply Avogadro's Law

Avogadro's Law states $\frac{V_1}{n_1} = \frac{V_2}{n_2}$, where $V_1 = 1.4\,\text{L}$, $n_1 = 2.3\,\text{mol}$, $V_2 = 7.2\,\text{L}$. Solve for $n_2$: $n_2 = \frac{V_2 \cdot n_1}{V_1}$.

Step2: Calculate $n_2$

Substitute values: $n_2 = \frac{7.2 \cdot 2.3}{1.4} \approx 11.74\,\text{mol}$. Wait, no—wait, the question is moles added, so $\Delta n = n_2 - n_1$. Wait, no, maybe I misread. Wait, original: started with 2.3 mol, 1.4 L. Final volume 7.2 L. Find moles added. So first find final moles $n_2$ via $\frac{V_1}{n_1}=\frac{V_2}{n_2} \implies n_2 = n_1 \cdot \frac{V_2}{V_1} = 2.3 \cdot \frac{7.2}{1.4} \approx 2.3 \cdot 5.1429 \approx 11.83\,\text{mol}$. Then moles added is $n_2 - n_1 = 11.83 - 2.3 \approx 9.53\,\text{mol}$, which is ~9.5.

Answer:

9.5 (the option with 9.5)