# If Sample 1 contains 2.98 moles of hydrogen at 35.1 degrees C and 2.3 atm in a 32.8 L container. How many moles of hydrogen are in a 45.3 liter container under the same conditions? Thank you for helping.

May 14, 2017

$\text{4.12 moles}$

#### Explanation:

You know that because the temperature and the pressure of the gas remain constant, you can use the fact that the volume of the container is directly proportional to the number of moles of gas as given by Avogadro's Law.

Mathematically, this is can be written as

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{{V}_{1} / {n}_{1} = {V}_{2} / {n}_{2}}}}$

Here

• ${V}_{1}$ and ${n}_{1}$ represent the volume and number of moles of gas at an initial state
• ${V}_{2}$ and ${n}_{2}$ represent the volume and the number of moles of gas at a final state

This means that when temperature and pressure are kept constant, increasing the number of moles of gas present in the container will cause its volume to increase.

Similarly, decreasing the number of moles of gas present in the container will cause its volume to decrease.

In your case, the volume of the container increased

$\text{32.8 L " -> " 45.3 L}$

you can say that the number of moles of gas present in the container must have increased.

Rearrange the equation to solve for ${n}_{2}$

${V}_{1} / {n}_{1} = {V}_{2} / {n}_{2} \implies {n}_{2} = {V}_{2} / {V}_{1} \cdot {n}_{1}$

Plug in your values to find

n_2 = (45.3 color(red)(cancel(color(black)("L"))))/(32.8color(red)(cancel(color(black)("L")))) * "2.98 moles" = color(darkgreen)(ul(color(black)("4.12 moles")))#

The answer is rounded to three sig figs.