A gas 'X' is collected over water at 17 degree C and 750mm. pressure. If volume of the gas is 50cc., calculate the volume of the dry gas at S.T.P. (at 17 degree C the vapour pressure is 14mm.)
Use (P1V1/T1) = (P2V2/T2)
P1 = (750-14)/760 atm
P2 = 1 atm
T1 = 273+17 = ?
T2 = 273
V1 = 0.050L
V2 = ? L and convert to mL if desired.
43.1 cc
To calculate the volume of the dry gas at standard temperature and pressure (STP), we first need to calculate the partial pressure of the gas X.
1. Start by subtracting the vapor pressure of water at 17°C (14 mmHg) from the total pressure (750 mmHg) to get the partial pressure of gas X:
Partial pressure of gas X = Total pressure - Vapor pressure of water
Partial pressure of gas X = 750 mmHg - 14 mmHg
Partial pressure of gas X = 736 mmHg
2. Now we can use the ideal gas law to calculate the volume of the gas X at STP. The ideal gas law equation is:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Universal gas constant
T = Temperature
3. At STP, the pressure is 1 atmosphere (760 mmHg) and the temperature is 0°C or 273 K. We can use these values in the equation.
P₁V₁ / T₁ = P₂V₂ / T₂
Where:
P₁ = Partial pressure of gas X at 17°C
V₁ = Volume of gas X at 17°C
T₁ = Temperature in Kelvin at 17°C
P₂ = Pressure at STP (1 atm or 760 mmHg)
V₂ = Volume of dry gas at STP
T₂ = Temperature in Kelvin at STP (0°C or 273 K)
4. Rearranging the equation to solve for V₂ (volume of dry gas at STP), we get:
V₂ = (P₁V₁T₂) / (T₁P₂)
Plug in the values:
V₂ = (736 mmHg * 50 cc * 273 K) / (290 K * 760 mmHg)
5. Calculate the value using the provided values:
V₂ = (736 * 50 * 273) / (290 * 760)
V₂ ≈ 73.48 cc
Therefore, the volume of the dry gas at STP is approximately 73.48 cc.