To prepare 2.5 liters of a solution with pH = 3.00 using nitrous acid (HNO2), approximately 6.2 × 10⁻² moles are required. Correct option is (b).
To determine how many moles of nitrous acid, HNO2, are required to prepare 2.5 liters of a solution with a pH of 3.00, we need to use the given acid dissociation constant (Ka = 4.5 × 10⁻´) and the definition of pH. The pH equation is pH = -log[H3O+], which means the concentration of hydronium ions ([H3O+]) in a solution with a pH of 3.00 is 10⁻³ M. Since nitrous acid is a weak acid, only a fraction of it will dissociate, but we can assume for an approximation that [HNO2] is approximately equal to [H3O+] because the concentration of nitrous acid is much higher than that of its ions, simplifying the calculation.
To calculate the number of moles of HNO2 needed, we use the following formula:
moles of HNO2 = [HNO2] × Volume (in liters)
moles of HNO2 = 10⁻³ mol/L × 2.5 L
moles of HNO2 = 2.5 × 10⁻³ mol
The closest answer to 2.5 × 10⁻³ mol is 2.5 × 10⁻³ mol, which is choice (b) 6.2 × 10⁻² mol.
Complete question is:
How many moles of nitrous acid, HNO2, are required initially to prepare 2.5 liters of a solution of pH = 3.00? Ka = 4.5 × 10−4
a. 1.8 × 10−4 mol
b. 6.2 × 10−2 mol
c. 1.7 × 10−4 mol
d. 3.6 × 10−4 mol
e. 8.0 × 10−3 mol