Question

On the basis of thermochemical equations (a), (b) and (c), find out which of the algebric relationships given in options (i) to (iv) is correct. (1) $ {C (graphite) + O_2(g) -> CO_2(g); \Delta_rH = x \, kJ \, mol^{-1}}$ (2) $ {C(graphite) + \frac{1}{2} O_2(g) -> CO (g); \Delta_rH = y \, kJ \, mol^{-1}}$ (3) $ {CO (g) + \frac{1}{2} O_2 (g) -> CO_2 (g); }$

• A. z = x + y
• B. x = y - z
• C. x = y + z
• D. y = 2z - x

Answer 1

The Correct Option is C

To solve the given problem, we must analyze the thermochemical equations provided and derive the correct algebraic relationship between them using Hess's Law. Hess's Law states that the total enthalpy change for a reaction is the same, no matter how it occurs in steps. Let's break down the equations and apply Hess's Law to determine which relationship is correct.

1. The given thermochemical equations are:
   1. {C (graphite) + O_2(g) \rightarrow CO_2(g); \Delta_rH = x \, kJ \, mol^{-1}}
   2. {C(graphite) + \frac{1}{2} O_2(g) \rightarrow CO (g); \Delta_rH = y \, kJ \, mol^{-1}}
   3. {CO (g) + \frac{1}{2} O_2 (g) \rightarrow CO_2 (g); \Delta_rH = z \, kJ \, mol^{-1}}
2. We need to find the correct relationship among options: z = x + y, x = y - z, x = y + z, y = 2z - x.
3. According to Hess's Law, combining equations (2) and (3) must equal equation (1):
   1. Adding equations (2) and (3):
      C (graphite) + \frac{1}{2} O_2(g) → CO (g); \Delta_rH = y
      CO (g) + \frac{1}{2} O_2 (g) → CO₂ (g); \Delta_rH = z
      Adding results in:
      C (graphite) + O₂(g) → CO₂(g); \Delta_rH = y + z
4. Comparing this resultant equation with equation (1), we see:
   C (graphite) + O₂(g) → CO₂(g); \Delta_rH = x
   This implies that the enthalpy change from combining equations (2) and (3) should be equal to equation (1):
   x = y + z
5. Hence, the correct relationship based on Hess's Law is x = y + z, which matches with equation combination. Therefore, option x = y + z is the correct choice.