An ideal gas has an initial volume of 500 cm3
, an initial temperature of 20◦C, and an initial
pressure of 2 atm. What is its final pressure if the volume is allowed to expand to 1000 cm3
while the temperature increases to 60◦C?
To solve this problem, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
First, let's convert the initial volume of 500 cm^3 to liters by dividing by 1000:
Initial volume (V1) = 500 cm^3 / 1000 = 0.5 L
Next, let's convert the initial temperature of 20°C to Kelvin by adding 273.15:
Initial temperature (T1) = 20°C + 273.15 = 293.15 K
We can also convert the final volume of 1000 cm^3 to liters:
Final volume (V2) = 1000 cm^3 / 1000 = 1 L
Now, the problem states that the temperature increases to 60°C, so let's convert that to Kelvin as well:
Final temperature (T2) = 60°C + 273.15 = 333.15 K
Since the number of moles of gas (n) remains constant, we can cancel it out from the equation.
Using the ideal gas law equation, we can set up the following equation:
(P1 * V1) / T1 = (P2 * V2) / T2
Substituting the known values:
(2 atm * 0.5 L) / 293.15 K = (P2 * 1 L) / 333.15 K
Now, we can solve for P2, the final pressure:
P2 = (2 atm * 0.5 L * 333.15 K) / (1 L * 293.15 K)
P2 = 3.61 atm
Therefore, the final pressure of the gas is approximately 3.61 atm when the volume expands to 1000 cm^3 and the temperature increases to 60°C.
The gas is ideal, so we can use the formula
P1 * V1 / T1 = P2 * V2 / T2
where
P1 and P2 = initial and final pressures respectively
V1 and V2 = initial and final volumes respectively
T1 and T2 = initial and final absolute temperatures respectively
Note that the temperature must be absolute, or the units must be in Kelvin. To convert Celsius units to Kelvin units, just add 273.
Substituting,
2 * 500 / (20+273) = (P2) * 1000 / (60+273)
Now solve for P2. Units in atm.
hope this helps~ `u`