What equation would I use to solve this problem: The volume of a balloon is 3.78 L at 22.8°C. The balloon is heated to 42.4°C. Calculate the new volume of the balloon.
To solve this problem, you would need to use the ideal gas law equation, which relates the pressure (P), volume (V), number of moles (n), and temperature (T) of a gas. The ideal gas law equation is expressed as:
PV = nRT
Where:
P = Pressure (in atm)
V = Volume (in liters)
n = Number of moles
R = Ideal gas constant (0.0821 L·atm/mol·K)
T = Temperature (in Kelvin)
However, in the given problem, we are not provided with the pressure or the number of moles. Therefore, we need to make an assumption that the pressure and the number of moles remain constant during the heating process. This assumption is reasonable if the balloon is considered to be a closed system.
We can rewrite the ideal gas law equation as:
V1/T1 = V2/T2
Where:
V1 = Initial volume (3.78 L)
T1 = Initial temperature (22.8°C converted to Kelvin by adding 273.15)
V2 = Final volume (which we want to calculate)
T2 = Final temperature (42.4°C converted to Kelvin by adding 273.15)
Now we can solve for V2:
V2 = (V1 * T2) / T1
Let's plug in the given values:
V2 = (3.78 * (42.4 + 273.15)) / (22.8 + 273.15)
By evaluating this equation, you can find the new volume (V2) of the balloon after it is heated to 42.4°C.
To solve this problem, you can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature if pressure and moles of gas are held constant. The equation for Charles's Law is:
V1/T1 = V2/T2
Where:
V1 = initial volume of the balloon
T1 = initial temperature in Kelvin
V2 = final volume of the balloon (the one you're trying to find)
T2 = final temperature in Kelvin
To use the equation, you need to convert temperatures from Celsius to Kelvin using the equation:
Kelvin = Celsius + 273.15
Let's calculate step-by-step.
Step 1: Convert temperatures to Kelvin
Initial temperature T1 = 22.8°C + 273.15 = 295.95 K
Final temperature T2 = 42.4°C + 273.15 = 315.55 K
Step 2: Plug the values into the equation
V1/T1 = V2/T2
3.78 L / 295.95 K = V2 / 315.55 K
Step 3: Cross-multiply and solve for V2
(3.78 L * 315.55 K) / 295.95 K = V2
397.2588 = V2
Step 4: Round the answer to an appropriate number of significant figures
The new volume of the balloon is approximately 397 L.
Therefore, the new volume of the balloon after being heated to 42.4°C would be approximately 397 L.