At 22.0 degrees Celsius , a student collects H2 gas in a gas collecting tube. The barometric pressure is 755.2mm Hg and the water levels inside and outside the tube are exactly equal. What is the total gas pressure in the gas collecting tube?
Total pressure is 755.2 as measured by the barometer. The total is composed of two partial pressures; i.e., that of the H2 gas + the water vapor at 22 C.
Ptotal = PH2 + PH2O. You can look up the vapor pressure of water in tables at various temperatures to find PH2O, then subtract from 755.2 to find the PH2 as a DRY gas (as opposed to the wet gas in the original problem.
To find the total gas pressure in the collecting tube, we need to consider both the barometric pressure and the pressure of the H2 gas collected.
The total gas pressure in the tube can be calculated using Dalton's law of partial pressures, which states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of each individual gas.
In this case, we can assume that the collected H2 gas is dry (contains no water vapor) and behaves ideally. Therefore, the partial pressure of H2 gas is equal to the total pressure in the tube.
First, let's convert the barometric pressure from mm Hg to atm, since atm is the commonly used unit for gases. The conversion factor is:
1 atm = 760 mm Hg
So, the barometric pressure is:
755.2 mm Hg x (1 atm / 760 mm Hg) = 0.9947 atm (rounded to 4 decimal places)
Next, let's calculate the pressure of the H2 gas using the ideal gas law equation:
PV = nRT
Where:
P = Pressure (in atm)
V = Volume (in liters)
n = Number of moles of gas
R = Ideal gas constant (0.0821 L·atm/mol·K)
T = Temperature in Kelvin
Since we don't have the volume or the number of moles of H2 gas, we can solve for the pressure (P) by rearranging the equation as follows:
P = nRT / V
To calculate the pressure, we need to know the number of moles of H2 gas. The number of moles can be found using the ideal gas law again:
PV = nRT
Rearranging the equation:
n = PV / RT
Let's substitute the given values into the equation:
P = 0.9947 atm (barometric pressure)
V = Volume of the gas collecting tube (not given)
R = 0.0821 L·atm/mol·K (ideal gas constant)
T = 22.0 + 273.15 Kelvin (temperature in Celsius converted to Kelvin)
Now, if you know the volume of the gas collecting tube, you can substitute it into the equation and calculate the pressure of the H2 gas using the given values. Otherwise, you need the volume information to find the total gas pressure.