A student is asked to bubble enough ammonia gas through...

A student is asked to bubble enough ammonia gas through water to make 4.00 L of an aqueous ammonia solution with a pH of 11.55 . What volume of ammonia gas at $25^{\circ} \mathrm{C}$ and 1.00 atm pressure is necessary?

Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental relation in physical chemistry that connects the pressure, volume, number of moles, and temperature of a gas. It is crucial for converting between the volume of a gas under specified conditions and the number of moles, which is often needed when relating gaseous reagents to their solution concentrations in chemical reactions.

Acid-Base Equilibrium

Acid-base equilibrium in aqueous solutions involves the balanced chemical reaction between a weak base (or acid) and water. For instance, when ammonia dissolves in water, it establishes an equilibrium by accepting a proton from water to form ammonium and hydroxide ions. This equilibrium concept is key for understanding how the concentration of the base and its conjugate acid affects the pH of the solution.

pH and pOH

pH is a measure of the acidity or basicity of a solution, defined as the negative logarithm of the hydrogen ion concentration. In aqueous solutions, pOH is related to pH by the relation pH + pOH = 14 at standard temperature. Understanding these concepts is essential to determine the concentration of hydroxide ions in a basic solution and to relate them to the overall properties of the solution.

Transcript

00:01 Okay, so we have a solution of ammonia, and we know that the ph of our solution is 11 .55, because this is a basic solution.

00:12 If i subtract that from 14, i can get the p -o -h, so that'll be 2 .45, and then i can get the concentration of hydroxide by just doing 10 to the negative 2 .45, and we'll get the hydroxide ion concentration is 0 .05, and we'll get the hydroxide ion concentration is 0 .0 .0 .5.

00:33 0355 molar.

00:36 So our ammonia is reacting with our water and our typical hydrolysis reaction here.

00:46 So it's going to make ammonium ion and hydroxide because it's a weak base.

00:53 If we look at what's happening through an ice box, we don't know how much nh3 we're going to use to start with.

01:01 We're going to ignore the water and we've got none of these to start with.

01:06 And we know that the hydroxide ion concentration, we just figured it out is 3 .55 times 10 of the minus 3.

01:15 Right.

01:16 So i must have gained 3 .55 times 10 of the negative 3.

01:23 Well, i would need to react and would produce this same amount here.

01:31 So obviously these values are going to be the same.

01:35 And at the same time, i must have used 3 .55.

01:40 Times 10 of negative 3.

01:43 So i end up with x minus 3 .55 times 10 of the negative 3 here.

01:51 So i'm going to go ahead and use our value for kb, which is 1 .8 times 10 to negative 5.

01:59 We'll set that up equal to products over reactants.

02:03 So 3 .55 times 10 to negative 3 .3...

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