6. the 3 variables p, v and t are interrelated. describe how each of the following changes affect gas…

Explanation:

6a)

According to Boyle's law ($P_1V_1 = P_2V_2$ for a fixed - amount of gas at constant temperature), when the volume $V$ increases, with the number of particles and temperature constant, the gas pressure $P$ decreases. This is because the gas particles have more space to move around, resulting in fewer collisions with the container walls per unit area.

6b)

From the ideal gas law $PV = nRT$ (where $n$ is the number of moles of gas, $R$ is the ideal gas constant), when the temperature $T$ increases with volume and number of particles constant, the pressure $P$ increases. As the temperature rises, the average kinetic energy of gas particles increases, causing them to collide more frequently and with greater force against the container walls.

6c)

With the ideal gas law $PV=nRT$, when the number of particles (i.e., $n$) increases with volume and temperature constant, the pressure $P$ increases. More particles mean more frequent collisions with the container walls, leading to higher pressure.

7)

We must use the absolute temperature scale (Kelvin) to solve gas problems because gas laws are based on the kinetic - molecular theory, where temperature is directly related to the average kinetic energy of gas particles. The zero point on the absolute temperature scale represents the state where gas particles have minimum kinetic energy (no translational motion). Using a non - absolute scale like Celsius or Fahrenheit would lead to incorrect results since these scales have an arbitrary zero point and negative values. For example, in the ideal gas law $PV = nRT$, if we used a non - absolute scale, we could get non - physical results such as negative pressures or volumes when the temperature is below the zero of that non - absolute scale.

7b)

From Gay - Lussac's law ($\frac{P_1}{T_1}=\frac{P_2}{T_2}$ for a fixed amount of gas at constant volume), $T_1 = 100\ K$, $T_2=50\ K$. [P_2=\frac{T_2}{T_1}P_1=\frac{50}{100}P_1 = 0.5P_1] The pressure is decreased by a factor of 2. Since the temperature is decreased and the volume and number of particles are constant, the average kinetic energy of the gas particles decreases, resulting in fewer and less forceful collisions with the container walls, so the pressure goes down.

7c)

From Charles's law ($\frac{V_1}{T_1}=\frac{V_2}{T_2}$ for a fixed amount of gas at constant pressure), $T_1 = 100\ K$, $T_2 = 50\ K$. [V_2=\frac{T_2}{T_1}V_1=\frac{50}{100}V_1=0.5V_1] The volume is decreased by a factor of 2. When the temperature is decreased with pressure and number of particles constant, the average kinetic energy of gas particles decreases. To maintain the same pressure (constant number of collisions per unit area), the volume must decrease.

Answer:

6a) Gas pressure decreases. Reason: More volume gives particles more space, reducing collision frequency with walls. 6b) Gas pressure increases. Reason: Higher temperature increases particle kinetic energy and collision force/frequency. 6c) Gas pressure increases. Reason: More particles lead to more frequent wall - collisions. 7) Use absolute temperature because gas laws are based on kinetic - molecular theory and non - absolute scales have arbitrary zeros. 7b) The pressure is decreased by a factor of 2. Pressure goes down as temperature decreases with constant volume and particle number, reducing particle kinetic energy and collision frequency/force. 7c) The volume is decreased by a factor of 2. Volume goes down as temperature decreases with constant pressure and particle number to maintain pressure.