Question:
Consider the following reaction:
\[ \text{CaCO}_3(s) \rightarrow \text{CaO}(s) + \text{CO}_2(g) \quad \Delta H = 178\text{ kJ} \]
The standard enthalpy of formation of $\text{CaCO}_3(s)$ and $\text{CO}_2(g)$ is $-1207$ and $-393\text{ kJ}\cdot\text{mol}^{-1}$ respectively. What is $\Delta_f H^\ominus$ (in $\text{kJ}\cdot\text{mol}^{-1}$) of $\text{CaO}(s)$?
Consider the following reaction:
\[ \text{CaCO}_3(s) \rightarrow \text{CaO}(s) + \text{CO}_2(g) \quad \Delta H = 178\text{ kJ} \]
The standard enthalpy of formation of $\text{CaCO}_3(s)$ and $\text{CO}_2(g)$ is $-1207$ and $-393\text{ kJ}\cdot\text{mol}^{-1}$ respectively. What is $\Delta_f H^\ominus$ (in $\text{kJ}\cdot\text{mol}^{-1}$) of $\text{CaO}(s)$?
Show Hint
Always ensure proper tracking of signs ($+$ and $-$) in thermochemistry problems.
A common error is forgetting to change the sign of the reactants when subtracting.
A common error is forgetting to change the sign of the reactants when subtracting.
Updated On: Jul 22, 2026
- $-636$
- $+636$
- $-814$
- $+814$
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Understanding the Question:
This is a thermochemistry question.
We need to calculate the standard enthalpy of formation of calcium oxide (CaO) using the enthalpy of decomposition of calcium carbonate ($\text{CaCO}_3$) and the enthalpies of formation of the other participants.
Step 2: Key Formula or Approach:
Using Hess's law, the standard enthalpy change of any chemical reaction is given by:
\[ \Delta_r H^\ominus = \sum \Delta_f H^\ominus (\text{products}) - \sum \Delta_f H^\ominus (\text{reactants}) \] For the given reaction:
\[ \Delta_r H^\ominus = \left[ \Delta_f H^\ominus(\text{CaO}(s)) + \Delta_f H^\ominus(\text{CO}_2(g)) \right] - \Delta_f H^\ominus(\text{CaCO}_3(s)) \]
Step 3: Detailed Explanation:
• Let us identify the given values:
Reaction Enthalpy ($\Delta_r H^\ominus$) = $+178\text{ kJ}\cdot\text{mol}^{-1}$
$\Delta_f H^\ominus(\text{CaCO}_3(s))$ = $-1207\text{ kJ}\cdot\text{mol}^{-1}$
$\Delta_f H^\ominus(\text{CO}_2(g))$ = $-393\text{ kJ}\cdot\text{mol}^{-1}$
• Let $x$ be the standard enthalpy of formation of $\text{CaO}(s)$.
• Substitute these values into the Hess's Law equation:
\[ 178 = \left[ x + (-393) \right] - (-1207) \] \[ 178 = x - 393 + 1207 \] \[ 178 = x + 814 \]
• Solving for $x$:
\[ x = 178 - 814 \] \[ x = -636\text{ kJ}\cdot\text{mol}^{-1} \]
Step 4: Final Answer:
The standard enthalpy of formation of $\text{CaO}(s)$ is $-636\text{ kJ}\cdot\text{mol}^{-1}$.
This is a thermochemistry question.
We need to calculate the standard enthalpy of formation of calcium oxide (CaO) using the enthalpy of decomposition of calcium carbonate ($\text{CaCO}_3$) and the enthalpies of formation of the other participants.
Step 2: Key Formula or Approach:
Using Hess's law, the standard enthalpy change of any chemical reaction is given by:
\[ \Delta_r H^\ominus = \sum \Delta_f H^\ominus (\text{products}) - \sum \Delta_f H^\ominus (\text{reactants}) \] For the given reaction:
\[ \Delta_r H^\ominus = \left[ \Delta_f H^\ominus(\text{CaO}(s)) + \Delta_f H^\ominus(\text{CO}_2(g)) \right] - \Delta_f H^\ominus(\text{CaCO}_3(s)) \]
Step 3: Detailed Explanation:
• Let us identify the given values:
Reaction Enthalpy ($\Delta_r H^\ominus$) = $+178\text{ kJ}\cdot\text{mol}^{-1}$
$\Delta_f H^\ominus(\text{CaCO}_3(s))$ = $-1207\text{ kJ}\cdot\text{mol}^{-1}$
$\Delta_f H^\ominus(\text{CO}_2(g))$ = $-393\text{ kJ}\cdot\text{mol}^{-1}$
• Let $x$ be the standard enthalpy of formation of $\text{CaO}(s)$.
• Substitute these values into the Hess's Law equation:
\[ 178 = \left[ x + (-393) \right] - (-1207) \] \[ 178 = x - 393 + 1207 \] \[ 178 = x + 814 \]
• Solving for $x$:
\[ x = 178 - 814 \] \[ x = -636\text{ kJ}\cdot\text{mol}^{-1} \]
Step 4: Final Answer:
The standard enthalpy of formation of $\text{CaO}(s)$ is $-636\text{ kJ}\cdot\text{mol}^{-1}$.
Was this answer helpful?
0
0
Top AP EAPCET Chemistry Questions
- The four quantum numbers of the valence electron of potassium are :
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
- In which of the following the election gain enthalpy of elements is correctly arranged?
- The radii of $ \text{F,}{{\text{F}}^{-}}\text{O} $ and $ {{\text{O}}^{2-}} $ are in the order
- Which of the following has the highest first ionization potential?
View More Questions
Top AP EAPCET Thermochemistry Questions
- When 'X' g of graphite is completely burnt in a bomb calorimeter in excess of \( O_2 \) at 298 K and 1 atm pressure as given in the equation $$ \text{C(graphite)} + O_2(g) \rightarrow CO_2(g) $$ The temperature of calorimeter raised from 298 K to 302 K. If the heat capacity of the calorimeter and molar enthalpy change for the reaction at 1 atm and 298 K are 20.7 kJ K\(^{-1} \) and -248.4 kJ mol\(^{-1} \), 'X' in g is
- The enthalpy of atomization of \({CH}_3{NH}_2(g)\) is 2313 kJ mol\(^{-1}\). If \(\Delta_{{C-H}}^{\ominus}\) and \(\Delta_{{N-H}}^{\ominus}\) are 414 and 389 kJ mol\(^{-1}\) respectively, then \(\Delta_{{C-N}}^{\ominus}\) (in kJ mol\(^{-1}\)) will be:
- The value of \(\Delta_r H\) for the reaction:
\[ {N}_2{O}_4(g) + 3 {CO}(g) \rightarrow {N}_2{O}(g) + 3 {CO}_2(g) \] (in kJ) is:
(Given: Enthalpies of formation in kJ mol\(^{-1}\) are \({CO}(g) = -110\), \({CO}_2(g) = -393\), \({N}_2{O}(g) = 81\), and \({N}_2{O}_4(g) = 9.7\)) - For the following given equilibrium reaction, K\(_p\) is equal to 1076 at T(K). What is the value of T (in K)? \[ \text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g) \] Given that \( R = 0.082 \, \text{L atm K}^{-1} \text{mol}^{-1} \), \( K_p = 1076 \), the equation is: \[ K_p = 1076, \, R = 0.082 \, \text{L atm K}^{-1} \text{mol}^{-1} \]
- At T(K), \(K_{\text{sp}}\) of two ionic salts MX\(_2\) and MX is \(5 \times 10^{-13}\) and \(1.6 \times 10^{-11}\) respectively. The ratio of molar solubility of MX\(_2\) and MX is
View More Questions
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions