Magnesium metal reacts with HCl(aq) according to the equation: Mg(s) + 2 HCl(aq) → MgCl2(aq) + H2(g)
In an experiment to determine the ΔH for this reaction, 0.158 g of Mg metal is combined with an excess of HCl to make 100.0 mL of solution in a coffee cup calorimeter. Upon reaction, the temperature of the solution rises from 25.60 C to 32.80 C. Determine ΔH for the reaction of one mole of Mg. Give your answer in units of kJ to three significant figures. Assume a density of 1.00 g/mL and the specific heat capacity of water for the solution.
To determine ΔH for the reaction of one mole of Mg, we can use the equation:
ΔH = q / n
Where:
ΔH is the enthalpy change for the reaction (in kJ/mol)
q is the heat absorbed or released by the reaction (in kJ)
n is the number of moles of reactant (in moles)
First, let's calculate the heat absorbed or released by the reaction, q.
q = m * c * ΔT
Where:
q is the heat absorbed or released by the reaction (in kJ)
m is the mass of the solution (in grams)
c is the specific heat capacity of water (4.18 J/g°C)
ΔT is the change in temperature (in °C)
To find mass of the solution, we need to convert the volume of the solution to grams using its density.
Mass = volume * density
The volume of the solution can be found by converting the given volume from mL to L.
Volume = 100.0 mL = 100.0 mL * (1 L/1000 mL) = 0.1000 L
Now, let's calculate the mass of the solution.
Mass = 0.1000 L * 1.00 g/mL = 0.1000 g
Next, let's calculate ΔT.
ΔT = (final temperature - initial temperature)
ΔT = (32.80°C - 25.60°C) = 7.20°C
Now, let's calculate q using the equation:
q = 0.1000 g * 4.18 J/g°C * 7.20°C * (1 kJ/1000 J)
q = 0.0301 kJ
Since we are interested in the value of ΔH for one mole of Mg, we need to determine the number of moles of Mg used in the reaction.
Number of moles of Mg = mass of Mg / molar mass of Mg
The molar mass of Mg is 24.31 g/mol. So, let's calculate the number of moles of Mg used in the reaction.
Number of moles of Mg = 0.158 g / 24.31 g/mol = 0.00650 mol
Now, let's calculate ΔH using the equation:
ΔH = q / n
ΔH = 0.0301 kJ / 0.00650 mol
ΔH = 4.63 kJ/mol (rounded to three significant figures)
Therefore, the ΔH for the reaction of one mole of Mg is 4.63 kJ/mol.