How many milliliters of concentrated hydrochloric acid solution (36% hydrochloric acid by mass, density 1.18 g/mL) are needed to produce 4.7 L of a solution that has a pH of 2.08?

To determine how many milliliters of concentrated hydrochloric acid solution are needed to produce 4.7 L of a solution with a pH of 2.08, we'll need to use the concept of pH and the properties of the concentrated hydrochloric acid. First, let's calculate the concentration of H+ ions in a solution with a pH of 2.08. The pH is defined as: pH = -log[H+] So, we can rearrange this equation to find [H+]: [H+] = 10^(-pH) [H+] = 10^(-2.08) [H+] ≈ 0.00831 M (moles per liter) Now, we want to prepare 4.7 liters of a solution with this concentration of H+ ions using concentrated hydrochloric acid solution (36% hydrochloric acid by mass, density 1.18 g/mL). First, we need to find the molar mass of hydrochloric acid (HCl): HCl = 1 (for hydrogen) + 35.5 (for chlorine) = 36.5 g/mol Since the concentrated hydrochloric acid solution is 36% hydrochloric acid by mass, it means there are 36 grams of HCl in 100 grams of the solution. Now, let's calculate the molarity of the concentrated hydrochloric acid solution: Molarity = (grams of solute / molar mass) / (volume in liters) Molarity = (36 g / 36.5 g/mol) / (1 L) Molarity ≈ 0.986 M Now, we can use the formula: C1V1 = C2V2 where: C1 = initial concentration (0.986 M) V1 = initial volume (unknown, in milliliters) C2 = final concentration (0.00831 M) V2 = final volume (4.7 L) Let's solve for V1: 0.986 M * V1 = (0.00831 M) * (4.7 L) V1 ≈ (0.00831 M * 4.7 L) / 0.986 M V1 ≈ 0.0396 L Now, we need to convert this volume from liters to milliliters: 1 liter = 1000 milliliters So, V1 ≈ 0.0396 L * 1000 mL/L ≈ 39.6 mL Therefore, you would need approximately 39.6 milliliters of concentrated hydrochloric acid solution to produce 4.7 liters of a solution with a pH of 2.08.