A sample of 1.67 grams of Z is dissolved into 500 grams of water which is in a Styrofoam coffee cup. The temperature is monitored and is found to rise from 25.594◦C to 26.041◦C. What is �Hsolution for substance Z? Assume
no heat is lost/gained by the cup itself. The specific heat of water is 4.184 J/g·◦C and the molecular weight of Z is 146 g/mol.
Answer in units of kJ/mol of Z
q = mass H2O x specific heat H2O x (Tfinal-Tinitial). would convert q in J to q in kJ.
delta H soln in kJ/g = q from above/1.67g
delta H soln in kJ/mol = kJ/g x (146 g/1 mol) = ?
To find the �Hsolution for substance Z, we need to use the equation:
�Hsolution = q / n
Where:
�Hsolution is the enthalpy of solution in kJ/mol
q is the heat gained or lost by the water, expressed in J
n is the number of moles of substance Z
To find q, we can use the equation:
q = mcΔT
Where:
m is the mass of water in grams
c is the specific heat of water in J/g·°C
ΔT is the change in temperature of the water in °C
First, let's find q:
m = 500 g (mass of water)
c = 4.184 J/g·°C (specific heat of water)
ΔT = (26.041 °C - 25.594 °C) = 0.447 °C
q = (500 g)(4.184 J/g·°C)(0.447 °C)
= 933.586 J
Next, we need to find the number of moles (n) of substance Z. To do this, we'll use the equation:
n = mass (Z) / Molar mass (Z)
Given that the mass of Z is 1.67 grams and the molar mass of Z is 146 g/mol, we have:
n = 1.67 g / 146 g/mol
= 0.01143 mol
Now that we have both q and n, we can calculate the �Hsolution:
�Hsolution = 933.586 J / 0.01143 mol
= 81744.6 J/mol
To convert J to kJ, divide by 1000:
�Hsolution = 81.7446 kJ/mol
Therefore, the �Hsolution for substance Z is 81.7446 kJ/mol.