A 0.158 g sample of magnesium metal reacts completely with 100.0 mL of 1.0 M hydrochloric acid in a coffee cup calorimeter. The temperature of the solution rose from 25.6°C to 32.8°C. What is ∆Hrxn? Assume the specific heat of the solution is 4.184 J/mol-K and the density is 1.0 g/mL.
To find the enthalpy change (∆Hrxn) of the reaction, we can use the equation:
∆Hrxn = q / n
where q is the heat absorbed or released during the reaction and n is the number of moles of magnesium reacted.
First, let's calculate the heat absorbed or released (q) using the equation:
q = m × c × ∆T
where m is the mass of the solution, c is the specific heat of the solution, and ∆T is the change in temperature.
Given information:
Mass of magnesium (magnesium reacted) = 0.158 g
Volume of hydrochloric acid = 100.0 mL = 0.100 L
Concentration of hydrochloric acid = 1.0 M
Temperature change (∆T) = (final temperature - initial temperature) = 32.8°C - 25.6°C
First, convert the volume of hydrochloric acid to moles:
moles of HCl = concentration × volume
moles of HCl = 1.0 M × 0.100 L
Next, calculate the moles of magnesium reacted using the balanced chemical equation:
Mg + 2 HCl → MgCl2 + H2
From the equation, we see that 1 mole of magnesium reacts with 2 moles of hydrochloric acid. Therefore,
moles of Mg = (0.158 g Mg / molar mass of Mg)
Now, calculate the heat absorbed or released (q):
q = m × c × ∆T
Here, we need the mass of the solution. To get the mass of the solution, we need to know the density of the solution. Since the density is given as 1.0 g/mL, the mass of the solution will be equal to the volume measured in mL.
mass of solution = volume of solution × density
mass of solution = 100.0 mL × 1.0 g/mL
Finally, we can substitute the values into the equation for q:
q = (mass of solution) × c × ∆T
Now that we have the value of q, we can substitute it into the equation to find ∆Hrxn:
∆Hrxn = q / moles of Mg
Calculating the values:
moles of HCl = 1.0 M × 0.100 L = 0.100 moles
moles of Mg = (0.158 g Mg / molar mass of Mg)
mass of solution = 100.0 mL × 1.0 g/mL
q = (mass of solution) × c × ∆T
∆Hrxn = q / moles of Mg
Calculating each value individually:
molar mass of Mg = 24.31 g/mol
moles of Mg = (0.158 g Mg / 24.31 g/mol)
mass of solution = 100.0 mL × 1.0 g/mL
∆T = 32.8°C - 25.6°C = 7.2°C
Now, we can plug these values into the appropriate equations:
moles of Mg = (0.158 g / 24.31 g/mol) = 0.00650 mol (rounded to 4 significant figures)
mass of solution = 100.0 mL = 100.0 g
q = (100.0 g) × (4.184 J/g·K) × 7.2°C
∆Hrxn = (100.0 g × 4.184 J/g·K × 7.2°C) / 0.00650 mol
Please note that in the calculation, the change in temperature (∆T) was converted from Celsius to Kelvin (K) by adding 273.15 to the values.
After plugging in the numbers:
q = 3000.96 J
∆Hrxn = 461536.64 J/mol
Therefore, the enthalpy change (∆Hrxn) of the reaction is approximately 461536.64 J/mol.
To determine ∆Hrxn (the enthalpy change of the reaction), you can use the equation:
∆Hrxn = q / n
where:
q is the heat absorbed or released by the reaction
n is the number of moles of the limiting reactant
First, let's find the number of moles of magnesium (Mg) in the sample:
- Convert the mass of Mg from grams to moles using its molar mass.
- The molar mass of Mg is 24.31 g/mol.
Moles of Mg = 0.158 g / 24.31 g/mol
Next, let's find the heat absorbed or released by the reaction (q):
- The heat is determined using the equation q = m × c × ∆T.
- m is the mass of the solution in grams.
- c is the specific heat capacity of the solution in J/mol-K.
- ∆T is the change in temperature in Kelvin (K).
First, let's find the mass of the solution:
- The density (d) is given as 1.0 g/mL, which means 1 mL of solution has a mass of 1.0 g.
- Since we have 100.0 mL of solution, the mass is 100.0 g.
q = m × c × ∆T
Now, let's substitute the known values:
- m = 100.0 g
- c = 4.184 J/mol-K
- ∆T = final temperature - initial temperature = 32.8°C - 25.6°C
Finally, let's calculate ∆Hrxn:
∆Hrxn = q / n
Using the above equations and values, you can find ∆Hrxn.
Mg + 2HCl ==> MgCl2 + H2
q = mass H2O x specific heat solution x (Tfinal-Tinitial)
q is delta H. This will give you delta H for the reaction. Most of these problems, however, want delta H in kJ/mol and not just joules; i.e., they don't state the problem correctly and assume you know they want it in kJ/mol and not just kJ for the reaction in the problem.
(q/0.158)*atomic mass Mg will give you J/mol and you can convert that to kJ/mol.