This question aims to find the **moles** of **oxygen gas** in a **cylinder** after a **leak.** The moles of oxygen gas need to be determined at the **same pressure** inside the **cylinder.**

The question is based on the concepts of **Ideal Gas Law** and **Avogadro’s** **Law.** Ideal gas law states that the **volume** of any gas is **directly proportional** to the **number** of **moles** of oxygen gas when the **temperature** and **pressure** of the gas remain **constant.** Ideal gas law is given as:

** PV = nRT **

Avogadro’s law states that the **two gasses** with the same **temperature** and **pressure** will have the same number of **molecules** if their **volume** is the same. Avogadro’s law is given as:

\[ \dfrac{ V_1 }{ n_1 } = \dfrac{ V_2 }{ n_2 } \]

## Expert Answer

We can use **Avogadro’s law** to solve this problem considering the **oxygen gas** to be a separate gas after the **leak.** The information given in this problem is as follows:

\[ Volume\ of\ Oxygen\ V_1 = 11.6\ L \]

\[ Moles\ of\ Oxygen\ n_1 = 3.2\ mol \]

\[ Pressure\ of\ Oxygen\ P = 5.2\ atm \]

\[ Volume\ of\ Oxygen\ after\ Leak\ V_2 = 10.5\ L \]

We need to determine the **moles** of **oxygen** remaining after the leak first and then we can **deduct** that **amount** from the **original amount** to determine the **lost gas.**

We can use **Avogadro’s Law** as:

\[ \dfrac{ V_1 }{ n_1 } = \dfrac{ V_2 }{ n_2 } \]

\[ \dfrac{ 11.6 }{ 3.2 } = \dfrac{ 10.5 }{ n_2 } \]

\[ n_2 = \dfrac{ 3.2 \times 10.5 }{ 11.6 } \]

\[ n_2 = 2.9\ mol \]

Now that we know, how much **moles** of **oxygen** are **remaining,** we can deduct it from the **original amount.** The amount of oxygen **lost** during **leak** is:

\[ Moles\ of\ Lost\ = n_1\ -\ n_2 \]

\[ Moles\ of\ Lost\ = 3.2\ -\ 2.9 \]

\[ Moles\ of\ Lost\ = 0.3\ mol \]

## Numerical Result

The **moles** of **oxygen lost** during the **leak** while the **pressure** in the **cylinder** remained the **same** is calculated to be:

\[ Moles\ of\ Oxygen\ Lost\ = 0.3\ mol \]

## Example

A **cylinder containing** **5 L** of **hydrogen gas** containing **1.8** **moles** develops a **leak** . Find the amount of **hydrogen gas** remaining in the **cylinder** if the **volume** of **hydrogen gas** is now recorded to be **3.5** **L** while the pressure of **3 atm** remained the same.

The information given in this problem are as follows:

\[ Volume\ of\ Hydrogen\ V_1 = 5\ L \]

\[ Moles\ of\ Hydrogen\ n_1 = 1.8\ mol \]

\[ Pressure\ of\ Hydrogen\ P = 3\ atm \]

\[ Volume\ of\ Hydrogen\ after\ Leak\ V_2 = 3.5\ L \]

Using the **Avogadro’s Law,** we can determine the **number** of **moles** remaining in the **cylinder** after the **leak.**

\[ \dfrac{ V_1 }{ n_1 } = \dfrac{ V_2 }{ n_2 } \]

\[ \dfrac{ 5 }{ 1.8 } = \dfrac{ 3.5 }{ n_2 } \]

\[ n_2 = \dfrac{ 1.8 \times 3.5 }{ 5 } \]

\[ n_2 = 1.26\ mol \]

The remaining **amount** of **hydrogen gas** is **1.26 moles.**