A sample of gas collected at 25°C and 2atm pressure occupies 500ml, what would it occupy at Standard temperature and pressure (STP)?
p1v1/t1 = p2v2/t2
To find out what volume the gas would occupy at STP, we need to use the ideal gas law equation:
PV = nRT
where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = temperature
At STP, the pressure is 1 atm and the temperature is 0°C or 273.15K.
First, let's calculate the number of moles (n) of gas in the given sample. We can use the ideal gas law equation for the known conditions:
P1 V1 = n R T1
P1 = 2 atm
V1 = 500 ml = 0.5 L
T1 = 25°C + 273.15 = 298.15K
Now we can rearrange the equation to solve for n:
n = (P1 V1) / (R T1)
Using the ideal gas constant R = 0.0821 L atm / (mol K), we get:
n = (2 atm * 0.5 L) / (0.0821 L atm / (mol K) * 298.15K)
n = 0.0405 mol
Now we can use this value of n in the ideal gas law equation at STP:
P2 = 1 atm
V2 = ?
T2 = 0°C + 273.15 = 273.15K
Rearranging the equation, we get:
V2 = (n R T2) / P2
Plugging in the values:
V2 = (0.0405 mol * 0.0821 L atm / (mol K) * 273.15K) / 1 atm
Simplifying the equation, we find:
V2 ≈ 1.09 L
Therefore, the gas would occupy approximately 1.09 liters at STP.