To solve the equation for \( x \), we need to expand and simplify the expression: Given: \[ 5.25 = \frac{x(2.80 + x)}{(3.20 - x)(6.00 - x)} \] First, expand both the numerator and the denominator: - Numerator: \( x(2.80 + x) = 2.80x + x^2 \) - Denominator: \( (3.20 - x)(6.00 - x) = 19.20 - 9.20x + x^2 \) Substitute these into the equilibrium expression: \[ 5.25 = \frac{2.80x + x^2}{19.20 - 9.20x + x^2} \] Cross-multiply to eliminate the fraction: \[ 5.25(19.20 - 9.20x + x^2) = 2.80x + x^2 \] Expand the left side: \[ 100.80 - 48.30x + 5.25x^2 = 2.80x + x^2 \] Rearrange all terms to one side: \[ 5.25x^2 - x^2 - 48.30x - 2.80x + 100.80 = 0 \] Simplify: \[ 4.25x^2 - 51.10x + 100.80 = 0 \] This is a quadratic equation in the form \( ax^2 + bx + c = 0 \), where: - \( a = 4.25 \) - \( b = -51.10 \) - \( c = 100.80 \) Use the quadratic formula to solve for \( x \): \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Calculate: \[ b^2 - 4ac = (-51.10)^2 - 4 \times 4.25 \times 100.80 \] \[ = 2612.21 - 1713.60 \] \[ = 898.61 \] Now, solve for \( x \): \[ x = \frac{51.10 \pm \sqrt{898.61}}{8.50} \] Calculate the square root and solve: \[ x = \frac{51.10 \pm 29.97}{8.50} \] This gives two potential solutions for \( x \): 1. \( x = \frac{51.10 + 29.97}{8.50} \approx 9.53 \) 2. \( x = \frac{51.10 - 29.97}{8.50} \approx 2.48 \) Since \( x \) must be less than the initial concentrations of Cl and CHCl, the feasible solution is \( x \approx 2.48 \). Therefore, the equilibrium molarity of HCl is approximately 2.48 M. Double check