A gas is at 35.0\deg C and 2.50 L. What is the temperature of the gas if the volume is increased to 5.00 L but pressure does not change?
The correct answer and explanation is:
To solve this, we use Charles’s Law, which states that for a fixed amount of gas at constant pressure, the volume of the gas is directly proportional to its temperature in Kelvin: V1T1=V2T2\frac{V_1}{T_1} = \frac{V_2}{T_2}
Given:
- Initial temperature, T1=35.0∘C=308.15 KT_1 = 35.0^\circ C = 308.15 \, K
- Initial volume, V1=2.50 LV_1 = 2.50 \, L
- Final volume, V2=5.00 LV_2 = 5.00 \, L
- Final temperature, T2=?T_2 = ?
- Pressure remains constant
Step-by-Step Solution:
Rearrange Charles’s Law to solve for T2T_2: T2=T1×V2V1T_2 = T_1 \times \frac{V_2}{V_1} T2=308.15 K×5.00 L2.50 LT_2 = 308.15 \, K \times \frac{5.00 \, L}{2.50 \, L} T2=308.15×2=616.30 KT_2 = 308.15 \times 2 = 616.30 \, K
Convert back to Celsius: T2=616.30−273.15=343.15∘CT_2 = 616.30 – 273.15 = \boxed{343.15^\circ C}
Explanation (300 Words):
When dealing with gases, it’s important to understand how temperature, pressure, and volume relate. One of the foundational gas laws that helps us analyze these relationships is Charles’s Law. This law explains how the volume of a gas increases with increasing temperature, provided the pressure and the amount of gas stay constant.
In this problem, a gas is initially at a temperature of 35.0°C and occupies a volume of 2.50 L. The volume is then increased to 5.00 L, and we’re asked to determine the new temperature assuming the pressure remains constant.
First, we must convert temperatures to the Kelvin scale, because gas laws require absolute temperature. This means converting 35.0°C to 308.15 K. Charles’s Law tells us that volume and temperature are directly proportional: if the volume doubles, the temperature must also double (in Kelvin).
Using the formula V1T1=V2T2\frac{V_1}{T_1} = \frac{V_2}{T_2}, we find that the final temperature is 616.30 K, which converts to 343.15°C. This is a significant increase in temperature, which makes sense because doubling the volume at constant pressure requires more energy — in the form of increased temperature — to maintain that pressure.
This result illustrates how gases expand when heated and how sensitive gas behavior is to temperature changes. It also highlights why heating a sealed gas container can be dangerous: the volume can’t increase, so pressure rises rapidly instead. Charles’s Law gives us a simple but powerful way to predict and understand such changes in real-world and laboratory situations.