Question

A chemist fills a reaction vessel with 0.534 g silver chromate Ag2CrO4 solid, 0.191 M silver Ag+ aqueous solution, and 0.823 M chromate CrO4−2 aqueous solution at a temperature of 25.0°C. Under these conditions, calculate the reaction free energy ΔG for the following chemical reaction: Ag2CrO4s +2Ag+aqCrO4−2aq Use the thermodynamic information in the ALEKS Data tab. Round your answer to the nearest kilojoule.

Answer 1

Answer:

$\large \boxed{\Delta G = \text{60 kJ}}$

Explanation:

              Ag₂CrO₄ ⇌ 2Ag⁺ + CrO₄²⁻; Ksp = 1.12× 10⁻¹²

I/mol·L⁻¹:                    0.191     0.823

To get ΔG under these conditions, we can use the equation

ΔG = ΔG° + RTlnQ = -RTlnK + RTlnQ = RTln[Q/K]

1. Calculate Q

$Q =\text{[Ag ^{+} ] ^{2} [Cr _{2} O _{4}^{2-} ]} = 0.191^{2}\times0.823 = 0.03002$

2. Calculate ΔG

T = (25.0 + 273.15) K = 298.15 K

$\begin{array}{rcl}\Delta G& =& RT \ln \left (\dfrac{Q}{K} \right )\\\\&=& 8.314 \times 298.15 \times \ln\left (\dfrac{0.03002}{1.12 \times 10^{-12}} \right )\\\\&=& 2479 \times \ln(2.860 \times10^{10})\\&=& 2479 \times 24.01\\& = & \text{59520 J}\\& = & \textbf{60 kJ} \\\end{array}\\\large \boxed{\mathbf{\Delta G} = \textbf{60 kJ}}$