What volume of H2 would be obtained at 27 degrees Celsius and 1.0 atm if 35.0 g of Fe reacts with 0.75 mil of H2SO4?
Equation:
2Fe + 3H2SO4 = 3H2 + Fe2(SO4)3
0.75 mol of H2SO4**
Determine the limiting reagent. Use that to find the mols H2 released and use PV = nRT to convert to V at the conditions listed.
To calculate the volume of H2 gas obtained, we need to 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)
Let's first calculate the number of moles of H2 gas produced using the given mass of Fe and the molar mass of Fe.
Step 1: Calculate the moles of Fe.
Given:
Mass of Fe = 35.0 g
Molar mass of Fe = 55.85 g/mol
Moles of Fe = (Mass of Fe) / (Molar mass of Fe)
= 35.0 g / 55.85 g/mol
= 0.626 mol
Step 2: Calculate the moles of H2 gas.
According to the balanced equation, 2 moles of Fe produces 3 moles of H2 gas.
Moles of H2 = (Moles of Fe) × (3 moles of H2 / 2 moles of Fe)
= 0.626 mol × (3/2)
= 0.939 mol
Step 3: Convert the given temperature from Celsius to Kelvin.
Given:
Temperature (in Celsius) = 27°C
Temperature (in Kelvin) = (Temperature in Celsius) + 273.15
= 27°C + 273.15
= 300.15 K
Step 4: Use the ideal gas law to find the volume of the gas.
Given:
Pressure (P) = 1.0 atm
Temperature (T) = 300.15 K
Number of moles (n) = 0.939 mol
Gas constant (R) = 0.0821 L·atm/(mol·K)
Rearranging the ideal gas law equation, we get:
V = (nRT) / P
V = (0.939 mol × 0.0821 L·atm/(mol·K) × 300.15 K) / 1.0 atm
V ≈ 23.39 L
Therefore, the volume of H2 gas obtained at 27 degrees Celsius and 1.0 atm, when 35.0 g of Fe reacts with 0.75 mol of H2SO4, is approximately 23.39 liters.
To calculate the volume of H2 gas produced in the reaction, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, let's calculate the number of moles of H2 gas produced:
Step 1: Calculate the number of moles of Fe. Given the mass of Fe (35.0 g) and its molar mass (55.85 g/mol), we can use the formula:
moles of Fe = mass of Fe / molar mass of Fe
moles of Fe = 35.0 g / 55.85 g/mol = 0.626 mol
Step 2: Use the stoichiometric coefficients of the balanced equation to find the number of moles of H2 gas produced. The balanced equation shows that 2 moles of Fe produce 3 moles of H2 gas:
moles of H2 gas = (moles of Fe) x (3/2)
moles of H2 gas = 0.626 mol x (3/2) = 0.939 mol
Step 3: Convert the temperature from Celsius to Kelvin. The Kelvin temperature is obtained by adding 273.15 to the Celsius temperature:
T = 27°C + 273.15 = 300.15 K
Now we can plug the values into the ideal gas law equation:
PV = nRT
V = (nRT) / P
V = (0.939 mol x 0.0821 L·atm/(mol·K) x 300.15 K) / 1.0 atm
V ≈ 22.8 L
Therefore, approximately 22.8 liters of H2 gas would be obtained at 27 degrees Celsius and 1.0 atm pressure when 35.0 g of Fe reacts with 0.75 mol of H2SO4.