A sample of Helium occupies 200 L at 30ºC under a pressure of 970 torr. What is the volume it occupies at standard temprature and pressure (STP)?
(P1V1)/T1 = (P2V2)/T2
Don't forget to change T to Kelvin.
Well, my friend, Helium is quite the party gas! Now, to answer your question, let's bring it back to standard temperature and pressure, or STP. At STP, the temperature is 0ºC (273 Kelvin) and the pressure is 1 atmosphere.
To find the volume at STP, we can use the ideal gas law: PV = nRT. Here, P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
To determine the number of moles, we need to find the molar mass of Helium (He), which is approximately 4 grams per mole.
Given that the initial volume (V1) is 200 L, the initial temperature (T1) is 30ºC (or 303 Kelvin), and the initial pressure (P1) is 970 torr, we can set up our equation like this:
(P1)(V1) / (n)(R)(T1) = (P2)(V2) / (n)(R)(T2)
Since we're looking for the volume at STP (V2), we'll substitute the values of P2, T2, and n later. Rearranging the equation, we get:
V2 = (P1)(V1)(T2) / (P2)(T1)
Substituting the given values, we have:
V2 = (970 torr)(200 L)(273 Kelvin) / (1 atm)(303 Kelvin)
Calculating this bad boy gives us a volume of approximately 179 L at STP. So there you have it - Helium enjoys a little shrinkage when it heads over to the standard temperature and pressure party!
To calculate the volume of the helium sample at standard temperature and pressure (STP), we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
At STP, the pressure is 1 atmosphere and the temperature is 0ºC or 273.15 Kelvin. We need to convert the given temperature from Celsius to Kelvin.
Given:
P1 = 970 torr
V1 = 200 L
T1 = 30ºC
Converting temperature:
T1 = 30ºC + 273.15 = 303.15 K
Substituting the given values into the formula, we have:
(P1)(V1) / T1 = (P2)(V2) / T2
(970 torr)(200 L) / 303.15 K = (1 atm)(V2) / 273.15 K
Simplifying, we get:
(970 torr)(200 L)(273.15 K) = (1 atm)(V2)(303.15 K)
Solving for V2:
V2 = (970 torr)(200 L)(273.15 K) / (1 atm)(303.15 K)
Now, we can calculate the volume of the helium sample at STP.
V2 = (970 torr)(200 L)(273.15 K) / (1 atm)(303.15 K)
V2 ≈ 161 L
Therefore, the sample of helium occupies approximately 161 liters at standard temperature and pressure (STP).
To determine the volume of helium at standard temperature and pressure (STP), we need to use the ideal gas law, which states:
PV = nRT
Where:
P = pressure
V = volume
n = moles of gas
R = ideal gas constant
T = temperature
First, let's convert the temperature from Celsius to Kelvin:
T(K) = T(ºC) + 273.15
Therefore, T(K) = 30 + 273.15 = 303.15 K
Next, we can plug the values into the ideal gas law equation:
PV = nRT
(970 torr)(200 L) = n(0.0821 L·atm/mol·K)(303.15 K)
Now, we can solve for n (the number of moles of helium):
(970 torr)(200 L) = n(0.0821 L·atm/mol·K)(303.15 K)
194,000 torr·L = n(24.871 L·atm/mol)
n = (194,000 torr·L) / (24.871 L·atm/mol)
n ≈ 7785.7 mol
Since 1 mole of any gas at STP occupies 22.4 L, we can calculate the volume:
V(STP) = n(22.4 L/mol)
V(STP) ≈ (7785.7 mol)(22.4 L/mol)
V(STP) ≈ 174,160 L
Therefore, the volume of the helium sample at standard temperature and pressure (STP) is approximately 174,160 L.