2 Ca(s) + O2(g) → 2 CaO(s) x
Ca(s) + CO2(g) + O2(g) → CaCO3(s) y
Based on the information in the table above, which of the following expressions is equivalent to AHran for the reaction represented below?
CaCO3(8)→ CaO (s) + CO2(g)
A) 8 12 +y
B )y
C )x+2y
D )x- 2y
The given reactions involve the formation of CaO and CaCO3. Looking at the coefficients, in the first equation, 2 moles of CaO are formed from 2 moles of Ca. In the second equation, 1 mole of CaO is formed from 1 mole of Ca. Therefore, we can infer that the formation of 1 mole of CaO releases half the energy (AHran) compared to the formation of 1 mole of CaO in the first equation.
Now, in the first equation, the formation of 2 moles of CaO releases energy represented by "2x". In the second equation, the formation of 1 mole of CaO releases energy represented by "x/2".
Therefore, the expression for AHran in the reaction CaCO3(s) → CaO(s) + CO2(g) would be
AHran = x/2 + y
The correct answer is C) x + 2y.
To determine the expression that is equivalent to AHran for the reaction CaCO3(s)→ CaO (s) + CO2(g), we need to look at the given reactions and their stoichiometry.
From the given equations:
2 Ca(s) + O2(g) → 2 CaO(s) (Equation x)
Ca(s) + CO2(g) + O2(g) → CaCO3(s) (Equation y)
We can see that Equation y is the combination of Equation x and the decomposition of CaCO3(s) into CaO(s) and CO2(g). Therefore, the change in enthalpy (AHran) for the decomposition of CaCO3(s) can be expressed as the sum of the change in enthalpy for Equation x (2 Ca(s) + O2(g) → 2 CaO(s)) and the change in enthalpy for the reverse reaction of Equation y.
The reverse reaction of Equation y is the formation of CaCO3(s) from CaO(s) and CO2(g). The stoichiometry of this reverse reaction is:
CaO(s) + CO2(g) → CaCO3(s)
To determine the expression equivalent to AHran, we need to consider the enthalpy changes for these reactions. Let's assign variables to represent the enthalpy changes as follows:
H1: Enthalpy change for Equation x (2 Ca(s) + O2(g) → 2 CaO(s))
H2: Enthalpy change for the formation of CaCO3(s) from CaO(s) and CO2(g) (CaCO3(s)← CaO(s) + CO2(g))
The overall enthalpy change (AHran) for the reaction CaCO3(s)→ CaO (s) + CO2(g) can be represented as:
AHran = H2 - H1
Now, let's look at the answer choices and substitute the corresponding expressions:
A) 8 + 12y
B) y
C) x + 2y
D) x - 2y
Since we determined that AHran = H2 - H1, the correct expression would be:
D) x - 2y
Therefore, the equivalent expression for AHran for the reaction CaCO3(s)→ CaO (s) + CO2(g) is x - 2y.
To find the expression for ΔH for the reaction CaCO3(s) → CaO(s) + CO2(g), we need to consider the given reactions and their stoichiometric coefficients.
From the first equation, 2 Ca(s) + O2(g) → 2 CaO(s), we can observe that the reaction produces 2 moles of CaO. Therefore, the enthalpy change (ΔH) for the formation of 2 moles of CaO can be represented as 2x.
From the second equation, Ca(s) + CO2(g) + O2(g) → CaCO3(s), we can observe that the reaction produces 1 mole of CaCO3. Therefore, the enthalpy change (ΔH) for the formation of 1 mole of CaCO3 can be represented as y.
Now, we want to find the expression for the enthalpy change (ΔH) for the reaction CaCO3(s) → CaO(s) + CO2(g).
Since 1 mole of CaCO3 produces 1 mole of CaO and 1 mole of CO2, we can write the expression for ΔH as:
ΔH for CaCO3(s) → CaO(s) + CO2(g) = ΔH(CaO) + ΔH(CO2)
Since ΔH(CaO) represents the enthalpy change for the formation of 2 moles of CaO and ΔH(CO2) represents the enthalpy change for the formation of 1 mole of CO2, the expression for ΔH can be written as:
ΔH for CaCO3(s) → CaO(s) + CO2(g) = 2x + y
Therefore, the correct answer is C) x + 2y.