Compute the change in temperature when 1.1 g of sodium chloride is dissolved in 200.0 mL of water initially at 28 C. The heat capacity of water is 4.184 J/mL/K. Neglect the heat capacity of the NaCl.
Species ΔfH (kJ/mol)
NaCl(aq)-407.3
NaCl(s) -411.2
DH = delta H.
DHsoln = DHsolvation - DHlatticeenergy
DHsoln = -407.3 -(-411.2) = 3.9 kJ/mol
The + means it is an endothermic reaction and the water will become cooler; we are extracting heat from the water. How much? 3.9 kJ/mol x (1000 J/kJ) x 1.1 g NaCl x (1 mol NaCl/molar mass NaCl) = q and since we are extracting heat it is -q.
Then -q = mass H2O x specific heat H2O x (Tfinal-Tinitial) and solve for Tfinal.
To compute the change in temperature, we need to use the equation:
q = m * C * ΔT
where:
- q is the heat transfer (in joules),
- m is the mass of the substance (in grams),
- C is the specific heat capacity of the substance (in J/g·K), and
- ΔT is the change in temperature (in Kelvin).
In this case, we are dissolving 1.1 g of sodium chloride (NaCl) in 200.0 mL of water. We need to find the change in temperature of the water.
First, convert the mass of water from milliliters to grams. The density of water is 1 g/mL, so using the mass-volume relationship:
Mass of water = Volume of water * Density of water
Mass of water = 200.0 mL * 1 g/mL
Mass of water = 200.0 g
Next, calculate the heat transfer, q, by rearranging the equation:
q = m * C * ΔT
ΔT = q / (m * C)
The heat capacity of water, C, is given as 4.184 J/mL/K. Since we have calculated the mass of water as 200.0 g, we can substitute the values into the equation:
ΔT = q / (m * C)
ΔT = q / (200.0 g * 4.184 J/g·K)
ΔT = q / 836.8 J·K⁻¹·g⁻¹
To find q, we need to calculate the heat transfer associated with dissolving 1.1 g of sodium chloride (NaCl). The enthalpy change of dissolving NaCl is given as -407.3 kJ/mol. Since we have the mass in grams, we can convert it to moles using the molar mass of NaCl:
Molar mass of NaCl = Na (22.99 g/mol) + Cl (35.45 g/mol)
Molar mass of NaCl = 58.44 g/mol
Moles of NaCl = Mass of NaCl / Molar mass of NaCl
Moles of NaCl = 1.1 g / 58.44 g/mol
Now, we can calculate the heat transfer q using the equation:
q = ΔH * moles of NaCl
q = -407.3 kJ/mol * (1.1 g / 58.44 g/mol)
Now that we have the value of q, we can substitute it back into the equation for ΔT:
ΔT = q / 836.8 J·K⁻¹·g⁻¹
Solving for ΔT will give you the change in temperature of the water when 1.1 g of NaCl is dissolved in 200.0 mL of water.