Answer:
ΔH/mol Cu(OH)₂= 34685.95 J/mol H₂O =34.68595 kJ/mol H₂O
Explanation:
The reaction that occurs in this case is:
CuSO₄ + 2 KOH → Cu(OH)₂ + K₂SO₄
The measurement and calculation of the amounts of heat exchanged by a system is called calorimetry. The equation that allows calculating these exchanges is:
Q=cmΔT
where Q is the heat exchanged for a body of mass m, constituted by a substance whose specific heat is c, and ΔT is the temperature variation experienced.
In this case:
- c=1 \(\frac{cal}{g*C}\)=4.184 \(\frac{J}{g*C}\) because the specific heat and density of the solution is the same as that
of water
Assuming that the total volume is the sum of the individual volumes then:
total volume= volume of CuSO₄ + volume of KOH = 150 mL + 150 mL
total volume= 300 mL
Given that the solution has the same density as water (1.00 \(\frac{g}{mL}\)) then
\(mass solution=300 mL*\frac{1 g}{1 mL}\)
mass solution = 300 g
- ΔT=31.3° C - 25.02 °C= 6.1° C
Then
Q = 300 g 4.184 \(\frac{J}{g*C}\)6.1° C =7656.72 J
On the other hand, the heat absorbed by the calorimeter is (
taking into account that to convert from degrees C to degrees K, 273.15 must be added):
24.2 \(\frac{J}{K}\) * [(31.3+273.15) - (25.2+273.15)] K = 147.62 J
So, the heat exchanged throughout the system is
Qsystem=7656.72 J + 147.62 J=7804.34 J
The reactants are present in their stoichiometric ratio, so there is no excess.
By reaction stochetry (that is, by the relationships between the molecules or elements that make up the reactants and reaction products) 1 mol of CuSO₄ produce 1 mol of Cu(OH)₂.
Knowing that moles of CuSO₄ are:
\(molesCuSO4=150 mL*\frac{1 L}{1000 mL}*\frac{1.50 mol}{1 L}\)
moles CuSO₄=0.225
You can apply the rule of three.
The rule of three or is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them. That is, what is intended with it is to find the fourth term of a proportion knowing the other three. Remember that proportionality is a constant relationship or ratio between different magnitudes.
If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied. To solve a direct rule of three, the following formula must be followed:
a ⇒ b
c ⇒ x
So
\(x=\frac{c*b}{a}\)
In this case: If 1 moles of Cu(OH)₂ are formed if 1 moles of CuSO₄ react, how many moles of Cu(OH)₂ will be formed if 0.049 moles of CuSO₄ react?
\(moles Cu(OH)2=\frac{0.225moles*1mol}{1 mol}\)
moles Cu(OH)₂=0.225 moles
Now
ΔH/mol Cu(OH)₂ = \(\frac{Qsystem}{moles Cu(OH)2} =\frac{7804.34 J}{0.225 moles}\)
ΔH/mol Cu(OH)₂= 34685.95 J/mol H₂O =34.68595 kJ/mol H₂O
The conversion was done remembering that 1 kJ = 1000 J
