Question

In a calorimetry experiment, 5.56g of sodium chloride are dissolved in 75.0mL of water at an initial temperature of 24.9℃. The final temperature of the solution is 23.7℃. What is the molar enthalpy of the solution of sodium chloride? (6 marks)

Answer 1

`-3.96\text{ KJ/mol}`

Step-by-step explanation:

Here, we want to get the molar enthalpy of the solution

We start by getting the change in enthalpy

Mathematically, we have that as follows:

`\Delta H\text{ = ms}\Delta T`

where:

m is the mass of water (we can get this by converting the volume given to liters and multiplying by 1000 g. This is same as 75 g)

Mathematically, this can be done as follows:

`\begin{gathered} 1000\text{ mL = 1 L} \\ 75\text{ mL to L will be:} \\ (75)/(1000)\text{ = 0.075 L} \end{gathered}`

Now, to convert this volume to mass, we multiply the volume above by 1000 g/L.

`\begin{gathered} 0.075\text{ L of water to g will be:} \\ 0.075\text{ L }*\text{ 1000 g/L = 75g} \end{gathered}`

s is the specific heat capacity of water which is 4.184 J/g °C

Delta T is the change in temperature which is (23.7 - 24.9) = -1.2°C

Substituting the values, we have it that:

`\Delta H\text{ = 75}*4.184\text{ }*(-1.2)\text{ = -376.56 J}`

To get the molar enthalpy of the solution, we have to divide the heat of reaction calculated above by the number of moles

The number of moles can be calculated by dividing the mass by the molar mass of sodium chloride

The molar mass of sodium chloride is 58.5 g/mol

The number of moles will be:

`\text{ number of moles = }\frac{mass}{molar\text{ mass}}\text{ = }(5.56)/(58.5)\text{ = 0.0950 mole}`

We now proceed to divide the amount of heat by this number of moles as follows:

`\text{ molar enthalpy = }\frac{heat\text{ of reaction}}{number\text{ of moles }}\text{ = }(-376.56)/(0.095)\text{ = -3.96 KJ/mol}`