Question

1. you have a gas in a container fitted with a piston and you change one of the conditions of the gas such that a change takes place, as shown below: state three distinct changes you can make to accomplish this, and explain why each would work.

Explanation:

Step1: Recall gas - law relationships

The ideal gas law is $PV = nRT$, where $P$ is pressure, $V$ is volume, $n$ is the number of moles of gas, $R$ is the ideal - gas constant, and $T$ is temperature. We want to double the volume ($V_2 = 2V_1$).

Step2: Decrease the pressure

If the number of moles $n$ and temperature $T$ are held constant, from $PV=nRT$, we have $P_1V_1 = P_2V_2$. If we want $V_2 = 2V_1$, then $P_2=\frac{1}{2}P_1$. So, decreasing the pressure to half of its original value while keeping $n$ and $T$ constant will double the volume because pressure and volume are inversely proportional ($P\propto\frac{1}{V}$) at constant $n$ and $T$ (Boyle's law: $PV = k$ where $k$ is a constant when $n$ and $T$ are fixed).

Step3: Increase the temperature

If the number of moles $n$ and pressure $P$ are held constant, from $PV=nRT$, we can write $\frac{V_1}{T_1}=\frac{V_2}{T_2}$ (Charles's law). If we want $V_2 = 2V_1$, then $T_2 = 2T_1$. So, doubling the temperature while keeping $n$ and $P$ constant will double the volume because volume and temperature are directly proportional ($V\propto T$) at constant $n$ and $P$.

Step4: Add more gas

If the pressure $P$ and temperature $T$ are held constant, from $PV=nRT$, we have $\frac{V_1}{n_1}=\frac{V_2}{n_2}$. If we want $V_2 = 2V_1$, then $n_2 = 2n_1$. So, doubling the number of moles of the gas while keeping $P$ and $T$ constant will double the volume because volume and the number of moles are directly proportional ($V\propto n$) at constant $P$ and $T$ (Avogadro's law: $V = kn$ where $k$ is a constant when $P$ and $T$ are fixed).

Answer:

1. Decrease the pressure to half of its original value while keeping the number of moles and temperature constant. Reason: According to Boyle's law ($PV = k$ at constant $n$ and $T$), pressure and volume are inversely proportional.
2. Double the temperature while keeping the number of moles and pressure constant. Reason: According to Charles's law ($\frac{V_1}{T_1}=\frac{V_2}{T_2}$ at constant $n$ and $P$), volume and temperature are directly proportional.
3. Double the number of moles of the gas while keeping the pressure and temperature constant. Reason: According to Avogadro's law ($\frac{V_1}{n_1}=\frac{V_2}{n_2}$ at constant $P$ and $T$), volume and the number of moles are directly proportional.