a gas has a volume of 4L at a temperature of -33 degrees C. if the temperature is increased to 27 degrees C and the pressure remains constant, what will be the new volume of the gas?
To find the new volume of the gas, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature at constant pressure.
Charles's Law formula: V1/T1 = V2/T2
Given:
V1 = 4 L (initial volume)
T1 = -33 degrees C (initial temperature)
T2 = 27 degrees C (final temperature)
We need to convert the temperatures to Kelvin since the Kelvin scale is used for temperature in gas laws.
Step 1: Convert the temperatures to Kelvin.
Initial temperature, T1 = -33 degrees C + 273.15 = 240.15 K
Final temperature, T2 = 27 degrees C + 273.15 = 300.15 K
Step 2: Use Charles's Law formula to find V2.
V1/T1 = V2/T2
Substitute the given values into the formula:
4 L / 240.15 K = V2 / 300.15 K
Step 3: Solve for V2.
Cross-multiply and solve for V2:
4 L * 300.15 K = V2 * 240.15 K
1200.6 K L = V2 * 240.15 K
Divide both sides by 240.15 K to solve for V2:
V2 = (1200.6 K L) / 240.15 K
V2 ≈ 4.996 L
Therefore, the new volume of the gas will be approximately 4.996 L when the temperature is increased to 27 degrees C while the pressure remains constant.
To solve this problem, we can use the combined gas law, which relates the pressure, volume, and temperature of a gas.
The combined gas law formula is:
(P1 × V1) / T1 = (P2 × V2) / T2
where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures.
Let's plug in the given values into the formula:
P1 is the initial pressure, which is constant and not given in the problem, and can be canceled out since it remains constant.
V1 is the initial volume, which is 4 L.
T1 is the initial temperature, which is -33 degrees Celsius. We need to convert it to Kelvin since the temperature must be in Kelvin for the calculation. To convert Celsius to Kelvin, add 273.15: T1 = -33 + 273.15 = 240.15 K.
T2 is the final temperature, which is 27 degrees Celsius. We need to convert it to Kelvin as well: T2 = 27 + 273.15 = 300.15 K.
Now we can rewrite the formula with the given values:
(4 L) / (240.15 K) = (V2) / (300.15 K)
To find V2, we can rearrange the formula:
V2 = (4 L) × (300.15 K) / (240.15 K)
Now we can calculate the new volume (V2):
V2 = (4 L) × (300.15 K) / (240.15 K)
V2 ≈ 5 L
Therefore, the new volume of the gas when the temperature is increased to 27 degrees Celsius while the pressure remains constant will be approximately 5 liters.
v1/t1 = v2/t2
Remember to use t1 and t2 is kelvin.
kelvin = degrees C + 273.15