Question

A balloon containing helium gas expands from 230 mL to 860 mL as more helium is added. What was the initial quantity of helium present if the expanded balloon contains 3.8 × 10-4 mol, assuming constant temperature and pressure? Which of the variables are known?

Answer 1

Using the Ideal Gas Law:

$pV=nRT\iff n=\dfrac{pV}{RT}$

Calculating the ratio between the initial and the final numbers of moles:

$\dfrac{n_1}{n_2}=\dfrac{\dfrac{p_1V_1}{RT_1}}{\dfrac{p_2V_2}{RT_2}}$

The statement says that $T_1=T_2,~p_1=p_2$. Hence:

$\dfrac{n_1}{n_2}=\dfrac{V_1}{V_2}\iff \dfrac{n_1}{3.8\times10^{-4}}=\dfrac{230}{860}\iff\\\\ n_1=\dfrac{3.8\times10^{-4}\times230}{860}\iff\boxed{n_1\approx1.0\times10^{-4}~mol}$

Answer 2

beginning volume and ending quantity of gas