The gas laws describe the behavior of gases under specific conditions of temperature, pressure, and volume. Three gas laws show the relationship between two variables when all others are held constant: Boyle’s law (pressure and volume are inversely proportional), Charles’s law (volume and temperature are directly proportional), and Gay-Lussac’s law (temperature and pressure are directly proportional).
The three laws can be combined into one law, called the combined gas law.
pressure times volume over temperature under conditions 1 equals pressure times volume over temperature under conditions 2
A sample of nitrogen has a volume of 1.75 L, a pressure of 2.00 atm, and a temperature of 35 °C. What is the new temperature, if the new volume is 2.45 L and the new pressure is 1.32 atm?
To solve for the new temperature using the combined gas law, we can set up the equation:
\( (P_1 \times V_1) / T_1 = (P_2 \times V_2) / T_2 \)
Plugging in the values we know:
\( (2.00 \text{ atm} \times 1.75 \text{ L}) / 308 \text{ K} = (1.32 \text{ atm} \times 2.45 \text{ L}) / T_2 \)
\( 3.5 \text{ atm} \cdot \text{L} / \text{K} = 3.24 \text{ atm} \cdot \text{L} / \text{K} / T_2 \)
Now, we can solve for T₂:
\( T_2 = (3.24 \text{ atm} \cdot \text{L} / \text{K}) / (3.5 \text{ atm} \cdot \text{L} / \text{K}) \)
\( T_2 = 0.9257 \text{ K} \)
Therefore, the new temperature, when the volume is 2.45 L and the pressure is 1.32 atm, is 0.9257 K.