A 1.000 L sample of HF gas at 20.0 °C and 0.601 atm pressure was dissolved in enough water to make 50.0 mL of hydrofluoric acid. (a) What is the pH of the solution?

Video transcript

Hello. In this problem, we are told in order to create 37 mL of hippo itis solution, a 1.5 liter sample of hippo. I'd I'd gas dissolved in 0.183 atmospheres of water at 27. degrees Celsius. Were asked to determine the ph of the solution. Given that the acid dissociation constant for hippo itis asset is 2.3 times 10 to minus 11. Let's begin by finding our moles of hippo iodide and then making use of that to find the initial concentration of our hippo itis acid. We are told that the temperature of our gas is 27.8°C. So let's convert that to Kelvin by adding 273. So that works out to 300 0. kelvin will now make use of the ideal gas equation since we have a sample of gas, So our pressure of gas is 0.183 atmospheres Volume We were told was 1.5 l Temperature is 328 Kelvin. And our our value 0.08206 leaders atmospheres and kelvin moore. We want to ensure that our units are canceling so atmospheres cancels, Leaders cancels kelvin cancels and we're left with goals, We have 0.0 moles. Then of our site. Now we'll find our initial concentration of Hippo Itis acid. So we have our 0.0111 moles of hyper I die which was placed in To water to create a solution of 37 mm. We want to convert our volume and familiars to leaders So 1000 ml The solution is equal to one l and setting up so that our units of liters of solution cancels. We find that we have a concentration of zero point 30056 Mueller. Now that's place what we know into an ice table. So we begin with our reaction. So the dissociation of our weak acid in water to form a journey mines and I put I die and I in we have initial change in equilibrium. So initially we have concentration is 0. miller of our hippo itis acid. We're gonna ignore the water since it's a pure liquid who initially have no majority of mines or no hippos and lions are changes minus X plus X plus X. We combined our initial and change to come up with our equilibrium. And then our next step we're going to use our acid dissociation constant to find a concentration of hydrogen mines at equilibrium. So as the dissociation constant. Then we have concentration of our products over that of our reactant and making use of what's in our ice table. This is X. I'm sex Over 0.30056 -1. Now, since we have a weak acid, we want to discern determine if we can simplify our calculation by eliminating the minus X. So we will check our simplifying assumption. So we'll check to check by taking our initial concentration of hyper itis acid and dividing it by our asset association constant. And if this is greater than 500, then we can eliminate minus X. So we have An initial concentration of 0.30056 And a acid dissociation cost of 2.3 times 10 to the -11. This works out to one 307 times to the 10, which is much greater than 500. And so we can then eliminate the X from our equation for acid dissociation constant and simplify our calculation. So we now have that R. K. A. Is equal to X squared over 0.30056. And we were told our Asset Association cost that was equal to 2.3 times 10 to the -11. So we will solve this for X. We will take the 0.30056 to the other side and then take the square root. And this works out to 2. times 10 to the -6, smaller. So this is equal to our adjoining mine concentration. So our last step we can calculate our ph it's our ph is equal to the negative log of our adjoining mine concentration, just 2.629 times 10 to the minus six. So this works out then to a ph of 5.58. The ph of this hippo itis acid solution is 5.58, and this corresponds to answer Thanks for watching. Hope this helps.