In 100 mL of 6.02 M HCl, which has a gravity of 1.10 g/ml, a strip of magnesium metal with a mass of 1.22 g dissolves. The initial temperature of the hydrochloric acid is 23.0 °C, and the end temperature of the solution is 45.5 °C. Calculate AH for the reaction under the conditions of the experiment. (The heat capacity of the calorimeter is 562 J/°C, specific heat of the finals is 4.184 /gºC.)
Mg(s) + HCl(aq) → MgCl2(aq) + H2(g)
Mg(s) + 2HCl(aq) → MgCl2(aq) + H2(g)
All of the 1.22 g Mg metal will dissolve.
mass solution = 100 mL x 1.10 g/mL = 110 g
q total = qrxn + Ccal*delta T
qtotal = (mass solution x specific heat solution x delta T) + Ccal*delta T
q = (110 g x 4.184 J/g*c x (45.5 - 23.0) + [562 J/c x (45.5-23.0)]
That is q for 1.22 g Mg.
Then convert to kJ/mol and you have it.
To calculate ΔH for the reaction, we need to use the equation:
ΔH = q / n
where ΔH is the enthalpy change (in J/mol), q is the heat transferred (in J), and n is the number of moles of the limiting reactant.
First, let's calculate the number of moles of magnesium (Mg) used in the reaction.
Given:
Mass of Mg = 1.22 g
Molar mass of Mg = 24.305 g/mol
Using the equation:
moles = mass / molar mass
moles of Mg = 1.22 g / 24.305 g/mol
moles of Mg = 0.0502 mol
Since the stoichiometry of the reaction is 1:1 between Mg and HCl, the number of moles of HCl used is also 0.0502 mol.
Next, let's calculate the amount of heat transferred in the reaction (q).
The heat transferred in the reaction can be calculated using the equation:
q = mcΔT
where q is the heat transferred (in J), m is the mass of the solution (in g), c is the specific heat capacity of the solution (in J/g°C), and ΔT is the change in temperature (in °C).
Given:
Volume of solution (V) = 100 mL = 100 g (since the density is 1.10 g/mL)
Specific heat capacity of the solution (c) = 4.184 J/g°C
Change in temperature (ΔT) = 45.5°C - 23.0°C = 22.5°C
Using the equation:
m = V x density
mass of solution (m) = 100 g x 1.10 g/mL
mass of solution (m) = 110 g
q = mcΔT
q = 110 g x 4.184 J/g°C x 22.5°C
q = 10,619 J
Now we have the value for q, the heat transferred.
Finally, we can calculate the enthalpy change (ΔH) for the reaction:
ΔH = q / n
ΔH = 10,619 J / 0.0502 mol
ΔH = 211,030 J/mol
Therefore, the enthalpy change (ΔH) for the reaction under the conditions of the experiment is 211,030 J/mol.
To calculate ΔH for the reaction, we can use the equation:
ΔH = q / moles
Step 1: Calculate the moles of magnesium metal (Mg) used.
Given:
Mass of magnesium (Mg) = 1.22 g
Molar mass of Mg = 24.31 g/mol
Moles of Mg = Mass / Molar mass
Moles of Mg = 1.22 g / 24.31 g/mol
Moles of Mg = 0.05 mol
Step 2: Calculate the amount of heat absorbed by the surroundings (q).
q = -C × ΔT
Given:
Initial temperature (T1) = 23.0 °C
Final temperature (T2) = 45.5 °C
Heat capacity of the calorimeter (C) = 562 J/°C
ΔT = T2 - T1
ΔT = 45.5 °C - 23.0 °C
ΔT = 22.5 °C
q = -C × ΔT
q = -562 J/°C × 22.5 °C
q = -12,645 J
Note: The negative sign indicates that heat is released by the reaction.
Step 3: Calculate the moles of hydrochloric acid (HCl) reacted.
Given:
Volume of HCl (V) = 100 mL
Density of HCl (ρ) = 1.10 g/mL
Molar mass of HCl = 36.46 g/mol
Concentration of HCl (C) = 6.02 M
First, calculate the mass of HCl used:
Mass of HCl = Volume × Density
Mass of HCl = 100 mL × 1.10 g/mL
Mass of HCl = 110 g
Next, calculate the moles of HCl:
Moles of HCl = Mass / Molar mass
Moles of HCl = 110 g / 36.46 g/mol
Moles of HCl = 3.02 mol
Step 4: Calculate ΔH for the reaction.
ΔH = q / Moles
ΔH = -12,645 J / (3.02 mol + 0.05 mol)
ΔH = -12,645 J / 3.07 mol
Finally, calculate ΔH:
ΔH = -4,118 J/mol (rounded to 4 significant figures)
Therefore, the enthalpy change (ΔH) for the reaction under the conditions of the experiment is approximately -4,118 J/mol.