A calorimeter contains 30.0 mL of water at 11.0 degrees C. When 1.50 g of X (a substance with a molar mass of 65.0 g/mol) is added, it dissolves via the reaction:
X (s)+H2O (l) ---> X (aq)
and the temperature of the solution increases to 26.0 degrees C.
Calculate the enthalpy change, Delta H, for this reaction per mole of X.
Assume that the specific heat and density of the resulting solution are equal to those of water [4.18 J/(g C) and 1.00 g/mL] and that no heat is lost to the calorimeter itself, nor to the surroundings.
I have been stuck on this question and have only 1 attempt left. I am unsure of the steps to get to the answer. Please explain?
q = mass H2O x specific heat H2O x (Tfinal-Tinitial)
Then delta H = q/g = q/1.50g
delta H/mol = (q/1.50)* 65.0 = ? J/mol
To calculate the enthalpy change, ΔH, for the reaction per mole of X, you need to calculate the heat gained or lost by the water in the calorimeter.
Here are the steps to solve this problem:
Step 1: Calculate the initial heat content of the water before the reaction.
- Use the formula: q1 = m1 * c1 * ΔT1
where q1 is the heat gained or lost by the water, m1 is the mass of the water, c1 is the specific heat capacity of water, and ΔT1 is the change in temperature of the water.
- The mass of water (m1) can be calculated using the density of water: m1 = V * density, where V is the volume of water and density is 1.00 g/mL.
- The specific heat capacity of water (c1) is given as 4.18 J/(g·°C).
- The change in temperature of the water (ΔT1) is the final temperature (26.0 °C) minus the initial temperature (11.0 °C).
Step 2: Calculate the heat change due to the dissolving of X.
- The heat change is equal to the heat gained by the water, so q2 = q1.
- Use the formula: q2 = m2 * c2 * ΔT2
where q2 is the heat change, m2 is the mass of X, c2 is the specific heat capacity of water, and ΔT2 is the change in temperature due to the dissolving of X.
- The mass of X (m2) is given as 1.50 g.
- The specific heat capacity of the solution (c2) is also given as 4.18 J/(g·°C).
- The change in temperature due to the dissolving of X (ΔT2) is the final temperature (26.0 °C) minus the initial temperature (11.0 °C).
Step 3: Calculate the enthalpy change per mole of X.
- The enthalpy change is equal to the heat change divided by the moles of X.
- The moles of X can be calculated using its molar mass (65.0 g/mol) and the mass added (1.50 g).
Step 4: Substitute the calculated values into the formula to obtain ΔH.
By following these steps, you should be able to find the enthalpy change per mole of X.