What is the pH and the principal source of H3O+ ions in 1.0 * 10-10 M HCl? (Hint: The pH of an acid solution can’t exceed 7.) What is the pH of 1.0 * 10-7 M HCl?

Video transcript

Welcome back everyone. Another video determine the Ph and identify the main source of hydro num in a 1.2 multiplied by S the power of negative nine molar solution of hydrochloric acid. Also determine the ph of 1.2 multiplied by s the power of negative C negative A hint ph should not exceed seven. So we have a two part problem. Let's begin with the first one. What we want to recall is that water undergoes auto ionization, meaning when two molecules of water combine, they produce hydro and hydroxide. So we want to keep this in mind throughout this problem. And we know that this process produces equal molarity of hydro and hydroxide. Specifically, we are producing 1.0 multiplied by the sense of the power of negative self throw names as well as 1.0 multiplied by sense. The power of negative seventh molar of hydroxide. Hydrochloric acid is a strong acid, meaning the concentration of hydro coming from hydrochloric acid would be the same as the concentration of hydrochloric acid itself because ST geometry tells us that HCL releases the same amount of H 30 plus. So the total amount of H 30 plus would be 1.0 multiplied by 10, the power of negative seventh molar coming from water and 1.2 multiplied by its sense of the power of negative ninth molar coming from HCL. When we add them, we notice that the additional quantity of hydro num coming from HCL is negligible. So we get approximately 1.0 multiplied by 10, the power of negative seventh molar total. And we know that Ph is equal to the negative logarithm of the concentration of hydro. In this case, this is 1.0 multiplied by 10, the power of negative seventh. And we get a Ph of 7.00. The main source of hydro num comes from water because the concentration of hydro coming from water is much larger than the concentration of hydro coming from HCL. And that would be our end. Now, for the second part, we noticed that the concentration of hydro num coming from HCL is much more significant because it is larger than the concentration of hydro num coming from water. So what should we do here? Well, essentially we need to introduce an IC table. Let's go ahead and take our auto ionization equation and solve for the concentration of hydro num. Here, we want to recall the common and effect. So let's introduce I CS. And essentially, since we have a larger quantity of HCL, we're going to say that the initial quantity of hydro would be coming from HCL since it completely ionizes and that would be 1.2 multiplied by 10 to the power of negative seventh molar. The initial molarity of oh minus before auto ionization takes place is zero. Right now, the change would be positive acts. We don't know what it is based on the common eye and the effect for each species based on stom Mery, it's 1 to 1. So the equilibrium concentrations would be 1.2 multiplied by 10 of the power of negative seventh plus X molar for hydro and for hydroxide, that would be X Mohler. And we know that KW the equilibrium constant for auto ionization is 1.0 multiplied by sense the power of negative 14th. So we're essentially going to express KW the product of X and 1.2 multiplied by 10 to the power of negative seventh plus X. This gives us the valley of KW. And now we simply want to solve this quadratic equation. So if we distribute our terms, we get X squared plus 1.2 multiplied by 10, the power of negative seventh X. And we're going to subtract 1.0 multiplied by 10 to the power of negative 14th to get the standard form of the quadratic equation which has coefficients of A, which is one, the leading coefficient B, the middle term which is 1.2 multiplied by negative seventh. And C the free term being negative 1.0 multiplied by. Since the power of negative 14th, when we use the quadratic equation formula, where basically the quadratic formula, we will obtain two solutions. One of them is going to be negative and it doesn't have any meaning because X should be positive. So we're only going to take the positive solution X is going to be equal to five point 662 multiplied byte sends the power of negative eight. So this is the additional quantity of hydro released in the auto ionization. And Ph would be the negative logarithm of the total concentration of hydro which is 1.2 multiplied by since the power of negative seventh plus the additional amount of 5.662 multiplied byte since the power of negative eight. And we can clearly see that HCL is responsible for the main source of hydro num. This gives us our final concentration of H 30 plus and the P value considering the Ph value, if we calculate the result, we get 6.75 in this case, which is our final answer. Thank you for watching.