A balloon contains 3.3 liters of nitrogen gas at a temperature of 90K and a pressure of 101 kPa.
If the temperature of the gas is allowed to increase to 25∘C and the pressure remains constant, what volume will the gas occupy?
V=_____L?
Ty again!
since PV/T is constant, if P is held constant, then V/T is constant.
if T is increased by a factor of 296/90, then V is increased by a factor of 296/90.
So, multiply 3.3 by that factor.
To find the final volume of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas (101 kPa)
V = initial volume of the gas (3.3 liters)
n = number of moles of gas
R = universal gas constant (0.0821 L·atm/(mol·K))
T = initial temperature of the gas (90 K)
First, let's calculate the number of moles of gas using the ideal gas law equation:
n = PV / RT
Substituting the given values:
n = (101 kPa) * (3.3 L) / ((0.0821 L·atm/(mol·K)) * (90 K))
Now, let's convert the pressure units from kPa to atm:
1 kPa = 0.00987 atm
Substituting:
n = (0.00987 atm) * (3.3 L) / ((0.0821 L·atm/(mol·K)) * (90 K))
Next, we'll convert the initial temperature from Kelvin (K) to Celsius (°C):
T(°C) = T(K) - 273.15
T(°C) = 90 K - 273.15
T(°C) = -183.15 °C
Now, we'll convert the final temperature from °C to Kelvin (K):
T(K) = T(°C) + 273.15
T(K) = 25 °C + 273.15
T(K) = 298.15 K
Now, let's find the final volume (Vf) when the pressure is constant:
Vf = (n * R * Tf) / Pf
Substituting the given values:
Vf = (n * (0.0821 L·atm/(mol·K)) * (298.15 K)) / (1 atm)
Finally, we can calculate the final volume:
Vf = [(0.00987 atm) * (3.3 L) / ((0.0821 L·atm/(mol·K)) * (90 K))] * [(0.0821 L·atm/(mol·K)) * (298.15 K)] / (1 atm)
Calculating this expression will give us the final volume of the gas in liters (L).
To solve this problem, we can use the combined gas law, which relates the initial and final conditions of a gas sample. The combined gas law equation is as follows:
(P1 * V1)/T1 = (P2 * V2)/T2
Where:
P1 is the initial pressure of the gas
V1 is the initial volume of the gas
T1 is the initial temperature of the gas
P2 is the final pressure of the gas (which remains constant in this case)
V2 is the final volume of the gas (what we are trying to find)
T2 is the final temperature of the gas
Let's plug in the values we have:
P1 = 101 kPa
V1 = 3.3 liters
T1 = 90 K
P2 = 101 kPa (constant pressure)
T2 = 25 °C = 25 + 273.15 = 298.15 K
Now we can solve for V2:
(P1 * V1) / T1 = (P2 * V2) / T2
(101 kPa * 3.3 L) / 90 K = (101 kPa * V2) / 298.15 K
V2 = [(101 kPa * 3.3 L) / 90 K] * 298.15 K / 101 kPa
V2 = (3.03 L)
Therefore, the gas will occupy approximately 3.03 liters when the temperature increases to 25 °C while the pressure remains constant.