If 4 moles of gas are added to a container that already holds 1 mole of gas, how will the pressure change inside the container?

Question

BlackTom AI · Accepted Answer

Consider the scenario: a gas inside a fixed-volume container with initial n_i = 1 mole. The pressure in an ideal gas at constant temperature and volume is proportional to the number of moles (P ∝ n).

Option 1: The pressure will be five times higher. Since the total number of moles becomes n_f = 5 (1 + 4), and temperature and volume are unchanged, the pressure increases in direct proportion to n. Therefore P_f = 5 P_i, which matches a fivefold increase.

Option 2: The pressure will double. Doubling would require the mole count to double to 2 moles, which is not the case here. The gas amount has increased from 1 to 5 moles, so this underestimates the change.

Option 3: The pressure will be four times higher. A fourfold rise would correspond to adding 3 moles (going from 1 to 4 total), but the container actually contains 5 total moles after the addition. This option ignores the full increase in n.

Option 4: The pressure will not change. If temperature and volume stay fixed but moles increase from 1 to 5, the pressure must rise accordingly; saying there is no change contradicts the fundamental relation between P and n under constant V and T.

In summary, with a fixed volume and constant temperature, pressure scales with the number of moles. Increasing from 1 mole to 5 moles produces a fivefold rise in pressure, aligning with the direct proportionality between P and n.

If 4 moles of gas are added to a container that already holds 1 mole of gas, how will the pressure change inside the container?单项选择题

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