In a constant pressure calorimeter, (cup calorimeter) a reaction occurred between sodium (23.00 g, 1.0mol) and water (1000 mL) based on the reaction shown below:
2Na(s) + 2H2O(l) → 2NaOH(aq) + H2(g)
The temperature of the resultant solution increases from 20.0 °C to 65.0 °C. If the volume of the solution remains as 1000 mL with a density of 1.02 g/mL and the specific heat changes of 4.00 J/g-°C. Calculate the enthalpy change for ther eaction in kJ/mol H2?
Hint: Use the mole ratio to determine the mol of H2 before calculating kJ/mol H2.
First, we need to calculate the amount of H2 produced in the reaction using the mole ratio:
2 moles of Na produces 1 mole of H2
So, the amount of H2 produced is 0.5 moles (since we have 1 mole of Na)
Next, we need to calculate the amount of heat released or absorbed by the reaction, which can be calculated using the following formula:
q = m * c * ΔT
where q = heat, m = mass, c = specific heat, and ΔT = change in temperature.
In this case, we can use the total mass of the solution (sodium + water) and the specific heat of water since sodium has a negligible specific heat compared to water. The mass of the solution can be calculated as:
mass = volume * density = 1000 mL * 1.02 g/mL = 1020 g
ΔT = 65.0 °C - 20.0 °C = 45.0 °C
q = 1020 g * 4.00 J/g-°C * 45.0 °C = 183600 J
Finally, we can calculate the enthalpy change of the reaction using the following formula:
ΔH = q / n
where n = moles of H2 produced.
ΔH = 183600 J / 0.5 mol = 367200 J/mol
However, the units need to be converted from J/mol to kJ/mol:
ΔH = 367.2 kJ/mol
Therefore, the enthalpy change for the reaction in kJ/mol H2 is 367.2 kJ/mol.
To calculate the enthalpy change for the reaction in kJ/mol H2, we need to follow these steps:
Step 1: Calculate the heat absorbed by the solution.
To do this, we use the formula:
q = mass × specific heat × change in temperature
The mass can be calculated by multiplying the volume (1000 mL) by the density (1.02 g/mL):
mass = volume × density = 1000 mL × 1.02 g/mL
Next, we calculate the change in temperature:
change in temperature = final temperature - initial temperature = 65.0 °C - 20.0 °C
Now, we can calculate the heat absorbed:
q = mass × specific heat × change in temperature
Step 2: Convert heat to kJ.
Since the specific heat is given in J/g-°C, we need to convert the heat from J to kJ by dividing by 1000:
q (in kJ) = q (in J) / 1000
Step 3: Determine the moles of H2.
According to the balanced equation, for every mole of H2 produced, 2 moles of Na are consumed. Therefore, the moles of H2 can be calculated by dividing the moles of Na by 2:
moles of H2 = moles of Na / 2
The moles of Na can be calculated using the given mass of Na and its molar mass:
moles of Na = mass of Na / molar mass of Na
Step 4: Calculate the enthalpy change per mole of H2.
The enthalpy change per mole of H2 is calculated by dividing the heat absorbed (q in kJ) by the moles of H2:
enthalpy change per mole of H2 = q (in kJ) / moles of H2
Now, let's perform the calculations:
Given:
Mass of Na = 23.00 g
Molar mass of Na = 22.99 g/mol
Volume of solution = 1000 mL
Density of solution = 1.02 g/mL
Specific heat = 4.00 J/g-°C
Initial temperature = 20.0 °C
Final temperature = 65.0 °C
Step 1: Calculate the heat absorbed by the solution.
mass = volume × density = 1000 mL × 1.02 g/mL = 1020 g
change in temperature = 65.0 °C - 20.0 °C = 45.0 °C
q = mass × specific heat × change in temperature = 1020 g × 4.00 J/g-°C × 45.0 °C
Step 2: Convert heat to kJ.
q (in kJ) = q (in J) / 1000
Step 3: Determine the moles of H2.
moles of Na = mass of Na / molar mass of Na
moles of H2 = moles of Na / 2
Step 4: Calculate the enthalpy change per mole of H2.
enthalpy change per mole of H2 = q (in kJ) / moles of H2
Performing these calculations will give you the enthalpy change for the reaction in kJ/mol H2.