Question

1. at 10.°c, 20.g of oxygen gas exerts a pressure of 2.1atm in a rigid, 7.0l cylinder. assuming ideal behavior, if the temperature of the gas was raised to 40.°c, which statement indicates the new pressure and explains why? a. 1.9 atm, because the pressure p decreases by the proportion $\frac{283}{313}$ b. 2.3 atm, because the pressure p increases by the proportion $\frac{313}{283}$ c. 0.52 atm, because the pressure p decreases by the proportion $\frac{10}{40}$ d. 8.4 atm, because the pressure p increases by the proportion $\frac{40}{10}$ 9. two sealed, rigid 5.0 l containers each contain a gas at the same temperature but at a different pressure, as shown above. also shown are the results of transferring the entire contents of container 1 to container 2. no gases escape during the transfer. assuming ideal behavior, which statement is correct regarding the total pressure of the gases after they are combined? a. the total pressure of the gases in the mixture is the sum of the initial pressures of oxygen gas and nitrogen gas because pressure only depends on the total amount of gas when volume and temperature are held constant. b. the total pressure of the gases in the mixture is lower than the sum of the initial pressures of oxygen and nitrogen because some of the energy of the particles will be lost due to an increase in the number of collisions. c. the total pressure of the gases in the mixture is higher than the sum of the initial pressures of oxygen and nitrogen because of the intermolecular forces that develop between oxygen and nitrogen molecules. d. the total pressure of the gases in the mixture cannot be determined because the actual value of the temperature is not given.

Explanation:

8.

Step1: Convert temperatures to Kelvin

Initial temperature $T_1=10 + 273=283\ K$, final temperature $T_2 = 40+ 273=313\ K$. For a rigid container (constant - volume), from the ideal - gas law $\frac{P_1}{T_1}=\frac{P_2}{T_2}$ (since $V$ and $n$ are constant, $P\propto T$).

Step2: Solve for the new pressure $P_2$

We know $P_1 = 2.1\ atm$, $T_1=283\ K$, $T_2 = 313\ K$. Rearranging the formula $\frac{P_1}{T_1}=\frac{P_2}{T_2}$ gives $P_2=P_1\times\frac{T_2}{T_1}$. Substituting the values, we have $P_2 = 2.1\times\frac{313}{283}\approx2.3\ atm$. The pressure increases by the proportion $\frac{313}{283}$ because pressure is directly proportional to temperature at constant volume for an ideal gas.

For ideal gases, when the volume and temperature are constant (as in this case, two rigid containers at the same temperature and the gases are combined in one of the containers), according to Dalton's law of partial pressures, the total pressure of a mixture of non - reacting ideal gases is the sum of the partial pressures of the individual gases. The partial pressure of a gas in a mixture is the pressure it would exert if it alone occupied the entire volume. Here, the partial pressure of oxygen is $P_{O_2}=0.8\ atm$ and the partial pressure of nitrogen is $P_{N_2}=1.0\ atm$. The total pressure $P_{total}=P_{O_2}+P_{N_2}$.

Answer:

B. 2.3 atm, because the pressure P increases by the proportion $\frac{313}{283}$

9.