Answer
$Q_c = K_c$. Therefore, the reaction mixture is exactly at equilibrium, and the solution is saturated. If we add more solid silver sulfate it will $not$ dissolve.
Work Step by Step
1. Determine the initial concentration of the ions.
$ Ag_2SO_4 $ : ( 107.9 $\times$ 2 )+ ( 16.00 $\times$ 4 )+ ( 32.07 $\times$ 1 )= 311.9 g/mol
- Calculate the amount of moles:
$$ 6.55 \space g \times \frac{1 \space mol}{ 311.9 \space g} = 0.0210 \space mol$$
- Calculate the molarity:
$$ \frac{ 0.0210 \space mol}{ 1.5 \space L} = 0.014 \space M $$
If all the substance dissolved:
$[Ag^{+}] = 2*0.014 \space M = 0.028 \space M$
$[S{O_4}^{2-}] = 0.014 \space M$
2. Determine the $Q_c$ of the reaction mixture:
- The exponent of each concentration is equal to its balance coefficient.
$$Q_C = \frac{[Products]}{[Reactants]} = [ Ag^{+} ] ^{ 2 }[ S{O_4}^{2-} ]$$
3. Substitute the values and calculate the constant value:
$$Q_C = ( 0.028 )^{ 2 }( 0.014 ) = 1.1 \times 10^{-5}$$
$Q_c = K_c$. Therefore, the reaction mixture is exactly at equilibrium, and the solution is saturated. If we add more solid silver sulfate it will not dissolve.
