What is the pH of a solution in which 224 mL of HCl(g), measured at 27.2 °C and 1.02 atm, is dissolved in 1.5 L of aqueous solution?

Video transcript

Hey everyone, we're asked to calculate the ph of a solution made by dissolving 100 and 50 mL of hydrochloric acid in its gaseous form at 0.95 atmospheric pressure and 25 degrees Celsius to make a 1.7 liter acquia solution. Here we have hydrologic acid in its gashes form and this is going to dissolve in water to make hydrologic acid in its earliest form. And as we've learned, we know that hydro acetic acid is a strong acid and we know that strong acids disassociate completely. So first we need to calculate the moles of our hydrologic acid to do so we can use the following formula pressure times volume equals the moles times our gas constant times our temperature. Now for our values, they told us our pressure is 0.95 atmospheric pressure. Our volume was set to be 100 and 50 mL. But since we want this in leaders, we can go ahead and convert it using dimensional analysis. Now we know that we have 10 to the third milliliters per one leader. So this means that our volume is going to come up to 0.150 liters. Now looking at our temperature, they gave it to us in C. So we have 25°C and we want to convert this into Kelvin. So we're going to add 273.15 and this will get us to 298.15 Kelvin. Now we want to go ahead and solve for our moles of hydrochloric acid. And this is going to be our pressure times volume all divided by our gas constant times our temperature. So plugging in those values we get 0. atmospheric pressure times are volume of 0.150 L, all divided by our gas constant which is 0.08-0 six leaders times atmospheric pressure divided by mole times kelvin. And this is going to be multiplied by 298.15 Kelvin which is our temperature. Now, when we calculate this out and cancel out all of our units, we end up with a value of 5.82436 times 10 to the negative third mole. Now we have our moles of hydrochloric acid. Now this is important because we're going to use this value to calculate the concentration of our hydrologic acid initially. So taking our moles of 5.82436 times 10 to the negative third mole. We're going to go ahead and divide this by our leaders which they provided to us. And this was said to be 1.7 leaders. Now this will give us a polarity of 3.42609 times 10 to the negative 3rd molar. Now that we have our polarity, we can go ahead and calculate our ph now we know that the concentration of our hydro ni um ion is essentially the same as the concentration of our hydrochloric acid initially since hydrologic acid is a strong acid and it dissociates completely. So again, this is equal to that value of 3.42609 times 10 to the negative 3rd molar. So to calculate our ph we're going to take the negative log of our concentration of our hydro knee um ion, Which is 3.42, times 10 to the negative third. Now this will get us to p. h. 2.47 and this will be our final answer. Now, I hope this made sense and let us know if you have any questions.