A sample of 2.08 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 25.682◦C to 25.899◦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 149 g/mol.
Answer in units of kJ/mol of Z
qH2O in J = mass H2O x specific heat H2O x dT.
Convert q in J to kJ.
dHZ = qH2O/g Z for dH/g Z
For dHZ in kJ/mol multiply dH/g x molar mass Z.
To find ∆Hsolution for substance Z, we can use the equation:
∆Hsolution = q / n
Where:
- q is the heat absorbed or released by the system
- n is the number of moles of substance Z
First, let's calculate the heat absorbed or released by the system using the equation:
q = m × c × ∆T
Where:
- m is the mass of water (500 g)
- c is the specific heat of water (4.184 J/g·°C)
- ∆T is the change in temperature (∆T = Tfinal - Tinitial)
∆T = 25.899°C - 25.682°C = 0.217°C
q = 500 g × 4.184 J/g·°C × 0.217°C
q = 455.62 J
Next, let's calculate the number of moles of substance Z using its molecular weight and the given mass:
n = m / M
Where:
- m is the mass of substance Z (2.08 g)
- M is the molecular weight of Z (149 g/mol)
n = 2.08 g / 149 g/mol
n = 0.0139 mol
Finally, we can calculate ∆Hsolution:
∆Hsolution = q / n
∆Hsolution = 455.62 J / 0.0139 mol
∆Hsolution ≈ 32789.93 J/mol
To convert this to kJ/mol, divide by 1000:
∆Hsolution ≈ 32.79 kJ/mol
Therefore, the ∆Hsolution for substance Z is approximately 32.79 kJ/mol.
To find the ∆Hsolution for substance Z, we can use the equation:
∆Hsolution = q / n
Where ∆Hsolution is the enthalpy change for the solution, q is the heat absorbed or released by the solution, and n is the number of moles of substance Z.
First, let's calculate the heat absorbed or released by the solution (q) using the equation:
q = m * c * ΔT
Where q is the heat, m is the mass of water, c is the specific heat of water, and ΔT is the change in temperature.
Given:
Mass of water (m) = 500 grams
Specific heat of water (c) = 4.184 J/g·°C
Change in temperature (ΔT) = 25.899°C - 25.682°C = 0.217°C
Plugging these values into the equation, we have:
q = 500 g * 4.184 J/g·°C * 0.217°C
Next, we need to calculate the number of moles of substance Z (n), using the equation:
n = m / M
Where n is the number of moles, m is the mass of substance Z, and M is the molar mass of substance Z.
Given:
Mass of substance Z (m) = 2.08 grams
Molar mass of substance Z (M) = 149 g/mol
Plugging these values into the equation, we have:
n = 2.08 g / 149 g/mol
Now, we can calculate ∆Hsolution using the equation:
∆Hsolution = q / n
Plugging the values of q and n into the equation, we have:
∆Hsolution = (500 g * 4.184 J/g·°C * 0.217°C) / (2.08 g / 149 g/mol)
Finally, to convert the answer to kJ/mol, we divide the answer by 1000:
∆Hsolution = ∆Hsolution / 1000
Now, calculate the value of ∆Hsolution using a calculator, and the answer will be in units of kJ/mol of Z.