Question

A gas at pressure of 19.4psi, 395mL and a temperature of 285K was subjected to a pressure of 31.7 psi and 400K. What is the volume (in ml) of the gas? a. 107 b. 201 c. 339 d. 2.13

Answer 1

The final volume of the gas when subjected to a pressure of 31.7 psi and 400 K is approximately 339 mL, using the combined gas law and converting units appropriately.

Step-by-step explanation:

To find the final volume of the gas, we can use the combined gas law, which is derived assuming the amount of gas (number of moles) remains constant:

`\(P_1 * V_1 / T_1 = P_2 * V_2 / T_2\)`

Where:

`\(P_1\) and \(V_1\)` are the initial pressure and volume,
`\(T_1\)` is the initial temperature,

`\(P_2\), \(V_2\), and \(T_2\)` are the final pressure, volume, and temperature, respectively.

First, we convert all units to standard:
1 atm = 14.6959 psi,
so,
`\(P_1 = 19.4 psi *`
`(1 atm / 14.6959 psi)\)`
and
`\(P_2 = 31.7 psi *`
`(1 atm / 14.6959 psi)\)`.

`Now, solving for \(V_2\):\\ \(V_2 = (P_1 * V_1 * T_2) / (P_2 * T_1)\)\\ \(V_2 = (19.4 psi / 14.6959 atm-psi * 395 mL * 400 K) / (31.7 psi / \\\\14.6959 atm-psi * 285 K)\)`

After calculations, we find
`\(V_2\)` to be approximately 339 mL, which matches option c.

Answer 2

Using the combined gas law, which states that the product of pressure and volume, divided by temperature, remains constant for a given amount of gas, the new volume of the gas when subjected to a pressure of 31.7 psi and a temperature of 400K is calculated to be approximately 201mL.

Step-by-step explanation:

To find the new volume of the gas when it is subjected to a pressure of 31.7 psi and a temperature of 400K, we can use the combined gas law, which states that the product of the pressure and volume divided by the temperature of a gas is constant, provided the amount of gas doesn't change.

The combined gas law formula is:
(P1 * V1) / T1 = (P2 * V2) / T2

We have the initial conditions: P1 = 19.4psi, V1 = 395mL, T1 = 285K, and the final conditions: P2 = 31.7psi, T2 = 400K. We need to find V2. Plugging in the values we get:

19.4psi * 395mL / 285K = 31.7psi * V2 / 400K

Multiplying both sides by 400K and dividing by 31.7psi, we can solve for V2:

V2 = (19.4psi * 395mL * 400K) / (285K * 31.7psi)

After calculating, we find that V2 = approximately 201mL.