Ammonium formate, HCOONH4, is a salt of a weak acid (K_a = 1.8x 10^-4) and a weak base (K_b = 1.8x 10^-5). Use h = dfracsqrtK_h1+sqrtK_h with K_h = K_w/(K_a K_b) for any concentration. Report h x 10^3 to two decimals.

JEE Advanced levelNumerical answerDifficulty 3 of 3ia125

Ammonium formate, $HCOONH X_{4}$ , is a salt of a weak acid ( $K_{a} = 1.8 \times 1 0^{- 4}$ ) and a weak base ( $K_{b} = 1.8 \times 1 0^{- 5}$ ). Use $h = \frac{K _{h}}{1 + K _{h}}$ with $K_{h} = K_{w} / (K_{a} K_{b})$ for any concentration. Report $h \times 1 0^{3}$ to two decimals.

Numerical answer type, tolerance 0.01.

K_{h} = K_{w} / (K_{a} K_{b}) = 3.09 \times 1 0^{- 6}

K_{h} = 0.00176

h = 0.00176/ (1 + 0.00176) = 0.001754

, so

h \times 1 0^{3} = 1.75