Hydrogen gas was collected in a gas-collecting bottle with a volume of 30.0 mL by water displacement on a day where the temperature was 24ºC and the barometric pressure was 98.125 kPa. The vapour pressure of water at 24ºC is 2.99 kPa. What would be the volume of hydrogen gas at STP if it was dry
Well, if the hydrogen gas is feeling a little dry, maybe it needs a good moisturizer. But let's focus on the question at hand.
To find the volume of hydrogen gas at STP (Standard Temperature and Pressure), we can use the combined gas law. The equation is:
(P₁ * V₁) / T₁ = (P₂ * V₂) / T₂
Where P₁, V₁, and T₁ are the pressure, volume, and temperature of the gas at one condition, and P₂, V₂, and T₂ are the pressure, volume, and temperature of the gas at the other condition.
First, we need to convert the temperature from Celsius to Kelvin, so T₁ = 24℃ + 273.15K = 297.15K. And since we're dealing with STP, we know that T₂ = 273.15K.
Next, we need to calculate the pressure at STP. The barometric pressure is given as 98.125 kPa, and the vapor pressure of water is 2.99 kPa. So the pressure of dry hydrogen gas is P₂ = 98.125 kPa - 2.99 kPa = 95.135 kPa.
The volume of the gas at the first condition is 30.0 mL.
Now we can plug in the values:
(98.125 kPa * 30.0 mL) / 297.15K = (95.135 kPa * V₂) / 273.15K
Solving for V₂ gives us:
V₂ = (98.125 kPa * 30.0 mL * 273.15K) / (297.15K * 95.135 kPa)
Crunching the numbers, we find that the volume of hydrogen gas at STP (if it were dry) is approximately 30.7 mL.
So, to recap: the volume of hydrogen gas at STP, if it were dry, would be 30.7 mL. Just remember, even hydrogen gas needs a bit of moisture to stay hydrated!
To find the volume of hydrogen gas at STP (Standard Temperature and Pressure), we need to apply the ideal gas law equation:
PV = nRT
where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (0.08206 L·atm/mol·K)
T = temperature in Kelvin
First, we need to find the number of moles of hydrogen gas using the given information:
1. Convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 24 + 273.15 = 297.15 K
2. Find the pressure of the collected hydrogen gas:
The actual pressure is the difference between the barometric pressure and the vapor pressure of water:
P_actual = P_barometric - P_vapor
P_actual = 98.125 kPa - 2.99 kPa
P_actual = 95.135 kPa
3. Convert the pressure to atm:
P_actual(atm) = P_actual(kPa) / 101.325
P_actual(atm) = 95.135 kPa / 101.325 = 0.93892 atm
4. Convert the volume to liters:
V(L) = V(mL) / 1000
V(L) = 30 mL / 1000 = 0.03 L
Now, we can calculate the number of moles of hydrogen gas:
PV = nRT
n = PV / RT
n = (0.93892 atm) * (0.03 L) / (0.08206 L·atm/mol·K) * (297.15 K)
n = 0.03627 mol
Finally, we can find the volume of dry hydrogen gas at STP by using the molar volume of a gas at STP, which is approximately 22.4 L/mol:
V_dry = n * V_molar
V_dry = 0.03627 mol * 22.4 L/mol
V_dry = 0.813 L
Therefore, the volume of dry hydrogen gas at STP would be approximately 0.813 liters.
To find the volume of hydrogen gas at STP, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
First, we need to calculate the number of moles of hydrogen gas using the collected volume of 30.0 mL and the given temperature and pressure.
Step 1: Correct for water vapor pressure
Since the collected gas is generated by water displacement, we need to correct for the vapor pressure of water at the given temperature. Subtracting the vapor pressure from the total pressure gives us the partial pressure of hydrogen gas.
Partial pressure of hydrogen gas = Total pressure - Vapor pressure of water
Partial pressure of hydrogen gas = 98.125 kPa - 2.99 kPa = 95.135 kPa
Step 2: Convert volume to liters
Since the ideal gas law requires volume in liters, we need to convert the collected volume from milliliters to liters.
Volume of hydrogen gas = 30.0 mL = 30.0 mL * (1 L / 1000 mL) = 0.0300 L
Step 3: Convert temperature to Kelvin
The ideal gas law requires temperature in Kelvin. To convert Celsius to Kelvin, we add 273.15.
Temperature in Kelvin = 24°C + 273.15 = 297.15 K
Step 4: Solve for moles of hydrogen gas
Now we can calculate the number of moles of hydrogen gas using the ideal gas law equation.
PV = nRT
n = PV / RT
n = (95.135 kPa * 0.0300 L) / (0.0821 L·kPa/mol·K * 297.15 K)
n = 0.08996 mol (rounded to 5 significant figures)
Step 5: Calculate volume at STP
Finally, we can use the number of moles (n) to find the volume of hydrogen gas at STP using Avogadro's law.
V1 / n1 = V2 / n2
V1 = volume at initial conditions
n1 = number of moles at initial conditions
V2 = volume at standard conditions (STP)
n2 = number of moles at standard conditions (STP)
Since we want to find the volume at STP, we can rearrange the equation as follows:
V2 = (V1 * n2) / n1
At STP, 1 mole of gas occupies 22.4 L. Therefore, n2 = 0.08996 mol and V1 = 0.0300 L.
V2 = (0.0300 L * 22.4 L/mol) / 0.08996 mol
V2 = 0.0749 L
So, the volume of dry hydrogen gas at STP would be approximately 0.0749 L.
(P1V1/T1) = (P2V2/T2)
Ptota = pH2 + pH2O. You are given Ptotal and pH2O.
98.125 = pH2 + 2.99
Solve for pH2(dry) and use that in the equation above. You know all but V2.