Boyle's Law: For a fixed mass of gas at constant temperature, the pressure of the gas is inversely…

Question

Boyle's Law: For a fixed mass of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. Mathematically, P 1/V or PV = constant.

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Boyle's Law: For a fixed mass of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. Mathematically, $P \propto \frac{1}{V}$ or $PV = \text{constant}$ .
Charles' Law: For a fixed mass of gas at constant pressure, the volume of the gas is directly proportional to its absolute temperature. Mathematically, $V \propto T$ or $\frac{V}{T} = \text{constant}$ .
Pressure Law (also known as Gay-Lussac's Law): For a fixed mass of gas at constant volume, the pressure of the gas is directly proportional to its absolute temperature. Mathematically, $P \propto T$ or $\frac{P}{T} = \text{constant}$ .

To calculate the pressure exerted by the gas and state the General Gas Equation:

Convert the given temperatures from Celsius to Kelvin.
$T_1 = 27^\circ\text{C} + 273 = 300 \text{ K}$ $T_2 = 90^\circ\text{C} + 273 = 363 \text{ K}$
Identify the given initial pressure.
$P_1 = 80 \text{ mmHg}$
Since the volume is maintained at constant, we use the Pressure Law (Gay-Lussac's Law), which states that $\frac{P_1}{T_1} = \frac{P_2}{T_2}$ .
Rearrange to solve for $P_2$ .
$P_2 = P_1 \times \frac{T_2}{T_1}$
Substitute the values and calculate the final pressure.
$P_2 = 80 \text{ mmHg} \times \frac{363 \text{ K}}{300 \text{ K}}$ $P_2 = 80 \times 1.21 \text{ mmHg}$ $P_2 = 96.8 \text{ mmHg}$
The pressure exerted by the gas is $\boxed{\text{96.8 mmHg}}$ .
State the General Gas Equation.
The General Gas Equation combines Boyle's Law, Charles' Law, and the Pressure Law. It is given by:
$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$

• Boyle's Law: For a fixed mass of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. Mathematically, P (1)/(V) or PV = constant.

Step-by-step solution

Convert the given temperatures from Celsius to Kelvin.

Identify the given initial pressure.

Since the volume is maintained at constant, we use the Pressure Law (Gay-Lussac's Law), which states that $\frac{P_1}{T_1} = \frac{P_2}{T_2}$ .

Substitute the values and calculate the final pressure.

State the General Gas Equation.

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