# What is the standard heat of formation of the nitrate ion, based on the standard enthalpy of formation of silver nitrate?

Given the standard enthalpy of formation of $$\ce{AgNO3(aq)} = \pu{-99 kJ/mol}$$ and the standard enthalpy of formation of $$\ce{Ag+(aq)} = \pu{+105 kJ/mol}$$, what's the standard heat of formation of $$\ce{NO3-(aq)}$$?

How can I know this if the standard enthalpy of reaction is not known? This is self test 10.1 in Atkins, PC.

Silver nitrate, $$\ce{AgNO3}$$ is a strong electrolyte. Based on the information given, I expect you are meant to assume that it dissociates completely when dissolved in water:

$$\ce{AgNO3(aq) -> Ag+(aq) + NO3- (aq)}$$

Thus, we can make the assumption that $$\ce{AgNO3(aq)} \equiv \ce{Ag+(aq) + NO3- (aq)}$$

Then, we can state:

$$\Delta_\mathrm{f} H (\ce{AgNO3(aq)}) = \Delta_\mathrm{f} H (\ce{Ag+(aq)})+\Delta_\mathrm{f} H (\ce{NO3- (aq)})$$

$$\implies \pu{-99kJ/mol} = \pu{+105kJ/mol} +\Delta_\mathrm{f} H (\ce{NO3- (aq)})$$

Thus $$\Delta_\mathrm{f} H (\ce{NO3- (aq)})=\pu{-204kJ/mol}$$