Question

A sample of oxygen gas at a pressure of 1.19 atm and a temperature of 24.4 °C, occupies a volume of 18.7 liters. If the gas is allowed to expand at constant temperature to a volume of 29.4 liters, the pressure of the gas sample will be ______ atm.

Answer 1

According to Boyle's law, for a given mass of ideal gas, pressure of gas is inversely proportional to the volume of gas, Provided the Temprature remains constant.

• P₁ = 1.19 atm
• P₂ = ?
• V₁ = 18.7 L
• V₂ = 29.4 L
• T = constant = 24.4° C = Isothermal process

`\implies \sf P_1 V_1 = P_2 V_2 \\`

`\implies \sf 1.19 * 18. 7= P_2 * 29.4 \\`

`\implies \sf 22.253= P_2 * 29.4 \\`

`\implies \sf P_2 = (22.253)/(29.4) \\`

`\implies \underline{ \red{\boxed{ \bf P_2 \approx0.756 \: atm }}} \\`

Answer 2

`\boxed {\boxed {\sf 0.757 \ atm}}`

Step-by-step explanation:

We are asked to find the pressure of a gas given a change in volume. Since the temperature remains constant, we are only concerned with volume and pressure. We will use Boyle's Law, which states the volume is inversely proportional to the pressure. The formula for this law is:

`P_1V_1= P_2V_2`

Initially, the oxygen gas occupies a volume of 18.7 liters at a pressure of 1.19 atmospheres.

`1.19 \ atm * 18.7 \ L = P_2V_2`

The gas expands to a volume of 29.4 liters, but the pressure is unknown.

`1.19 \ atm * 18.7 \ L = P_2 * 29.4 \ L`

We are solving for the new pressure, so we must isolate the variable
`P_2`. It is being multiplied by 29.4 liters. The inverse operation of multiplication is division. Divide both sides of the equation by 29.4 L.

`\frac {1.19 \ atm * 18.7 \ L}{29.4 \ L} =( P_2 * 29.4 \ L)/(29.4 \ L)`

`\frac {1.19 \ atm * 18.7 \ L}{29.4 \ L} =P_2`

The units of liters cancel.

`\frac {1.19 \ atm * 18.7 }{29.4 } =P_2`

`\frac {22.253}{29.4 } \ atm = P_2`

`0.7569047619 \ atm =P_2`

The original measurements all have 3 significant figures, so our answer must have the same. For the number we calculated, that is the thousandth place. The 9 in the ten-thousandth place to the right of this place tells us to round the 6 up to a 7.

`0.757 \ atm \approx P_2`

The pressure of the gas sample is approximately 0.757 atmospheres.