A solution is prepared by adding 50.0 mL concentrated...

A solution is prepared by adding 50.0 mL concentrated hydrochloric acid and 20.0 mL concentrated nitric acid to 300 mL water. More water is added until the final volume is 1.00 L . Calculate $\left[\mathrm{H}^{+}\right],\left[\mathrm{OH}^{-}\right]$, and the pH for this solution. [Hint: Concentrated HCl is $38 \% \mathrm{HCl}$ (by mass) and has a density of $1.19 \mathrm{~g} / \mathrm{mL}$; concentrated $\mathrm{HNO}_3$ is $70 . \% \mathrm{HNO}_3$ (by mass) and has a density of $1.42 \mathrm{~g} / \mathrm{mL}$.]

Key Concepts

Molarity Calculation

Molarity is the unit of concentration defined as the number of moles of a solute divided by the volume of the solution in liters. This concept is essential when determining how concentrated a solution is and is the basis for calculating chemical reactivity in solutions.

Strong Acid Behavior and Complete Dissociation

Strong acids, such as HCl and HNO?, dissociate completely in water, meaning that the entire amount of acid contributes to the hydrogen ion concentration in the solution. This principle allows one to assume that the moles of acid added are equivalent to the moles of hydronium ions generated, simplifying subsequent calculations.

pH and pOH Relationship

The pH scale quantifies the acidity or basicity of a solution by taking the negative logarithm of the hydrogen ion concentration. Additionally, pH and pOH are related through the equation pH + pOH = 14 (at 25°C), which provides a framework for converting between the concentrations of hydrogen ions and hydroxide ions.

Density and Percent Composition for Concentrated Solutions

The use of density and percent composition by mass is critical when converting the volume of a concentrated solution to the mass of the active ingredient. This mass is then converted to moles, forming the basis for further calculations in determining the resulting concentrations after dilution.

Dilution Principles

Dilution involves adding more solvent to a solution, thereby reducing the concentration of each solute proportionally to the increase in total volume. Understanding how dilution affects concentration is crucial for preparing solutions with desired molarity or pH.

Transcript

00:01 So this problem has a lot going on.

00:02 There's a few things to solve for, and there's a lot given in the problem.

00:07 There's a lot of information shared.

00:09 So set up a need -no equations table for this.

00:14 So need is a list of things we need to find.

00:17 No is a list of stuff we're given in the problem.

00:20 And then equations are things we can use to solve the problem based on the variables that we have, and the variables that we need to find.

00:28 So because there's so much, we really need to figure out a map of what we're going to do.

00:34 So the equations i just put c below.

00:38 So essentially, we need to work backwards.

00:41 We need to get the concentration of h plus.

00:46 And from there, we can get oh minus and ph.

00:48 So that's really our key.

00:50 How do we get concentration of h plus? from all of this, you know, we've got volume and density and percent by mass, lots of different stuff.

00:58 Well, in order to get concentration, i definitely need to be at moles.

01:03 And so i need to be able to get moles.

01:05 And when we're looking at concentration, we need moles and volume.

01:10 Well, already we do see that a volume is given of one liter.

01:13 So that's good.

01:14 We're headed in the right direction.

01:16 But how are we going to get moles of h -plus? well, we're going to have to find the moles of h -cl and moles of h -n -o -3 and add them together.

01:24 Because there's strong acids, the number of moles of acid will be equal to the number or moles of h plus.

01:31 Well, i'm also given something about mass.

01:33 I'm given a density, percent by mass, a volume.

01:37 So somewhere i'm going to have to get the masses of these two things and add them together.

01:41 And i can use the molar mass to go from mass to moles.

01:46 Well, how can i get mass? well, i'm going to have to get it from the density.

01:49 And then i know my density equation, d equals m over v.

01:53 We're also given a percent by mass.

01:55 So we can get the density of the solution.

01:58 We can use density of the solution to get the mass of the solution and then percent by mass to get the percent of acid in that solution.

02:08 So we've got a little bit of work to do here.

02:11 So the first thing we're going to do is we're going to take our hcl solution.

02:18 We're going to use density equals mass over volume to get the mass of the solution.

02:27 And so how we would do that, if we want to solve, for mass, so that would be density times volume is equal to mass.

02:39 So for, i already wrote, hcl.

02:43 So density of the hcl solution is 1 .19 grams per milliliter, and the volume that we have is 50 milliliters.

02:58 So if we do that math, 1 .19, 1 .19 times 50.

03:04 That's going to be 59 .5 grams of solution.

03:13 So 59 .5 grams times the percentage 38%.

03:20 That's how much hcl...

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