Question

a sample of nitrogen gas at 298 k and 745 torr has a volume of 37.42 l. what volume will it occupy if the pressure is increased to 894 torr at constant temperature?

Answer 1

The volume of the nitrogen gas will be 31.25 L when the pressure is increased to 894 torr at a constant temperature.

Step-by-step explanation:

When pressure and temperature are constant, Boyle's Law can be applied to relate the initial and final volumes and pressures. Boyle's Law states that the product of the initial pressure (P₁) and initial volume (V₁) is equal to the product of the final pressure (P₂) and final volume (V₂) for a given amount of gas.

Mathematically, Boyle's Law can be expressed as:

`\(P₁ \cdot V₁ = P₂ \cdot V₂\).`

Given that the initial volume (V₁) is 37.42 L, the initial pressure (P₁) is 745 torr, and the final pressure (P₂) is 894 torr, we can rearrange the formula to find the final volume (V₂):

`\[V₂ = \frac{{P₁ \cdot V₁}}{{P₂}}\]`

Substituting the given values into the equation:

`\[V₂ = \frac{{745 \, \text{{torr}} \cdot 37.42 \, \text{{L}}}}{{894 \, \text{{torr}}}} = 31.25 \, \text{{L}}\]`

Therefore, the final volume of the nitrogen gas, when the pressure is increased to 894 torr at a constant temperature, is 31.25 L.

Answer 2

To find the new volume of nitrogen gas after a pressure change at constant temperature, Boyle's Law is used. The relation P1 * V1 = P2 * V2 allows us to calculate the new volume by rearranging the formula to V2 = (P1 * V1) / P2. By plugging in the initial pressure, initial volume, and final pressure, we can determine the new volume.

Step-by-step explanation:

The question is asking to find the new volume of nitrogen gas when the pressure is changed while keeping the temperature constant, which can be solved using Boyle's Law. Boyle's Law states that for a fixed amount of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. This means that if the pressure increases, the volume decreases, and vice versa, assuming that the temperature and the amount of gas remain constant. The formula for Boyle's Law is P1 * V1 = P2 * V2, where P1 and V1 are the initial pressure and volume, respectively, and P2 and V2 are the final pressure and volume.

According to the given data:

• Initial pressure (P1): 745 torr
• Initial volume (V1): 37.42 L
• Final pressure (P2): 894 torr

We can rearrange the formula to solve for the final volume (V2):

V2 = (P1 * V1) / P2

Substituting the values from the question:

V2 = (745 torr * 37.42 L) / 894 torr

By performing the calculation, we can determine the new volume of the nitrogen gas after the pressure is increased to 894 torr at a constant temperature of 298 K.