The following reaction produces hydrogen gas: Fe (s) + 2HCl (aq) FeCl2 (aq) + H2 (g)The hydrogen gas from the reaction of 9.5 g of iron with excess acid is collected in a 10.0 L flask at 24°C. Atmospheric pressure in the lab is 752 torr. If the Vapor Pressure of water at this temperature is 22.4 torr, what is the volume (in mL) of the hydrogen gas in the flask?
To find the volume of the hydrogen gas in the flask, we need to determine the moles of hydrogen gas produced and then convert it to volume using the ideal gas law equation.
First, let's calculate the moles of hydrogen gas produced in the reaction using the given mass of iron.
Step 1: Calculate the moles of iron (Fe).
- The molar mass of iron (Fe) is 55.85 g/mol.
- The given mass of iron is 9.5 g.
- Use the formula: moles = mass / molar mass
- Substituting the values: moles of Fe = 9.5 g / 55.85 g/mol
Next, since the reaction ratio between Fe and H2 is 1:1, the moles of iron will be equal to the moles of hydrogen gas produced.
So, moles of H2 = moles of Fe
Now that we have the moles of hydrogen gas, we can calculate the volume using the ideal gas law equation:
PV = nRT
Where:
P = Pressure (in atm)
V = Volume (in liters)
n = Moles
R = Ideal Gas Constant (0.0821 L.atm/mol.K)
T = Temperature (in Kelvin)
Step 2: Convert the given pressure and temperature to atm and Kelvin.
- Given atmospheric pressure = 752 torr
- Vapor pressure of water (partial pressure) = 22.4 torr
To get the pressure for the hydrogen gas, subtract the vapor pressure of water from the atmospheric pressure.
- Hydrogen gas pressure = Atmospheric pressure - Vapor pressure of water
- Convert torr to atm: 1 atm = 760 torr
Step 3: Calculate the volume of the hydrogen gas.
- Rearrange the ideal gas law equation to solve for V: V = nRT / P
- Substitute the values calculated in the previous steps into the equation.
Finally, convert the volume from liters to milliliters by multiplying by 1000.
Please provide the temperature in Celsius or convert it to Kelvin for further calculation, and then I will walk you through the calculations.
To find the volume of hydrogen gas in the flask, we can use the ideal gas law equation:
PV = nRT
where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, we need to calculate the pressure of the hydrogen gas in the flask. The total pressure is the sum of the atmospheric pressure and the vapor pressure of water:
Total Pressure = Atmospheric Pressure + Vapor Pressure of Water
Total Pressure = 752 torr + 22.4 torr
Total Pressure = 774.4 torr
Next, we need to calculate the number of moles of hydrogen gas produced in the reaction. We can use the stoichiometry of the reaction to do this.
From the balanced equation:
1 mole of iron (Fe) produces 1 mole of hydrogen gas (H2)
Given that 9.5 g of iron reacts, we can calculate the number of moles using the molar mass of iron:
Molar mass of Fe = 55.845 g/mol
Number of moles of Fe = mass / molar mass
Number of moles of Fe = 9.5 g / 55.845 g/mol
Now we have the number of moles of hydrogen gas produced, which is also equal to the number of moles of FeCl2:
Number of moles of H2 = Number of moles of FeCl2
Now we have all the information needed to calculate the volume of hydrogen gas using the ideal gas law equation:
PV = nRT
Rearranging the equation:
V = (nRT) / P
Convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 24°C + 273.15
T(K) = 297.15 K
Substitute the values into the equation:
V = (nRT) / P
V = (number of moles of H2) x (gas constant) x (temperature in Kelvin) / (total pressure)
Convert the volume to mL:
Volume (mL) = V x 1000
Now, let's calculate the volume of hydrogen gas in the flask.