Answer:
[tex]\large \boxed{\text{1 mol/L}}[/tex]
Explanation:
We must use the Nernst equation
E_{\text{cell}} = E_{\text{cell}}^{\circ} - \dfrac{RT}{zF}\ln Q
We want Ecell < 0 for a reverse reaction, so assume it is 0.
Step 1. Calculate E°cell
Anode: 3Zn ⟶ 3Zn²⁺(4 mol·L⁻¹) + 6e⁻; E° = +0.7618 V
Cathode: 2Cr³⁺ (x mol·L⁻¹) + 6e⁻ ⟶ 2Cr; E° = -0.744 V
Overall: 3Zn + 2Cr³⁺(x mol·L⁻¹) ⟶ 3Zn²⁺(4 mol·L⁻¹) + 2Cr; E° = +0.018 V
Step 2. Calculate Q
[tex]\begin{array}{rcl}0 & = & 0.018 - \dfrac{8.314\times 298}{6 \times 96 485} \ln Q\\\\-0.18& = & -0.00428 \ln Q\\\ln Q & = & 4.16\\Q & = & e^{4.16}\\ & = & \mathbf{64.0}\\\end{array}[/tex]
3. Calculate [Cr³⁺]
[tex]\begin{array}{rcl}Q & = & \dfrac{\text{[Zn$^{2+}$]$^{3}$}}{\text{[Cr}^{3+}]^{2}}\\\\64.0 & = & \dfrac{4^{3}}{\text{[Cr}^{3+}]^{2}}\\\\\text{[Cr}^{3+}]^{2}& = & \dfrac{64}{64.0}\\\\& = & 1\\\text{[Cr}^{3+}] & = & \textbf{1 mol/L}\\\end{array}\\\text{[Cr$^{3+}$] must be less than $\large \boxed{\textbf{1 mol/L}}$ for the reaction to be spontaneous in the reverse}\\\text{direction.}[/tex]
