in today's lesson I want to go over a list of formulas and equations associated with acids and bases so let's begin if you know the H+ concentration you can calculate the pH using this formula it's negative log of the hydrogen ion concentration in water the concentration of H+ is the same as the concentration of the hydronium ion so it's important to know that the p is equal to the negative log of the hydroxide concentration and the pH plus the P this adds up to 14 now if you need to calculate the H+ concentration from pH you could use this formula it's 10 raised to the ph and if you need to calculate the hydroxide concentration it's 10 to the P now the concentration of H+ * ohus this is going to equal 1 * 10-4 which is equal to the auto ionization constant of water KW so water can react with itself one of the water molecules will accept a proton the other one will lose it so water can ionize into hydronium and hydroxide now this value holds true at 25° C so it could change with temperature now let's start about finding the pH of a weak acid let's say if you have a weak acid like HF or let's use a generic acid ha it's going to react with water and it's going to release a proton so what is going to acquire that proton turn into h2+ and we're going to get the conjugate base a minus now Ka the acid dissociation constant is going to equal the concentration of the products divided by the reactants h3o+ a minus and ha they they are in the aquous phase water is the liquid and we don't include solids or liquids in the equilibrium expression now if Ka is small particularly 10 to4 or less a lot of times you could simplify this equation and when that happens H+ the concentration of H+ is approximately the square root of H the concentration of ha time Ka so remember that's if Ka is less than 1 * 10us 4 typically this approximation will work once you know the H+ concentration you can calculate the pH using this formula now if Ka is small and you want to just go directly to the pH here's another formula that you could use the pH is equal to 12 the pka of the acid minus log of the concentration of the acid all in parentheses so that formula will just help you to go directly to the pH all you need to know is the conentration of the acid and the KA value now it's important to know that PKA is equal to log of Ka much in the same way that pH is negative log of the H+ concentration by the way for those of you who want all of these formulas and more uh feel free to check out the links in the description section below I'm going to post a direct link to the formula sheet where you can get all of these equations now let's talk about if we have a weak base a weak base will react with water we're going to get the conjugate acid of that weak base and hydroxide so for this reaction we're dealing with KB the base dissociation constant it's going to equal the concentration of HB Plus time hydroxide / the concentration of the base so just like before if KB is less than 10 to4 you can calculate the hydroxide concentration using this formula so it's uh approximately the square root of the concentration of the base times KB once you have the hydroxide concentration you can calculate the PO using this formula and once you know the P you could find a pH using this formula so three steps now for those of you who want to just use one step and get to the pH directly you could use this formula it's equal to 12 14 plus the pka here we have have KB you need to calculate Ka from KB so this is the pka of the conjugate acid whereas KB represents It's associated with the base the weak base so this is going to be 12 14 plus PKA and then plus log of the concentration of the base so that's how you can go directly to the pH if you know the concentration of the weak basee and the KB value but let's talk about how to get Ka from KB so Ka is going to be KW ID KB and KW is 1 * 10 -14 so that's how you can calculate Ka from KB and once you have Ka you could determine the pka so let's review those formulas again so we said that the pka is equal to negative log of Ka likewise the pkb is equal to negative log of KB now the pka plus the PK b equals to 14 much in the same way that pH plus p is 14 if you need to calculate Ka from PKA you could use this formula and KB is equal to 10 to the pkb and as mentioned before K * KB is equal to KW and KW is 1 * 104 at 25° and again you could find all of these formulas in the formula sheet down below now let's talk about a buffer solution if you have a weak base and the conjugate weak acid you have a buffer solution the pH of a buffer solution is equ Al to the pka plus log base over acid let me write this differently so this is the concentration of the base divided by the concentration of the acid now because we're dealing with a ratio here this could be in marity or in moles if it's in moles as long it's it's in the same solution which means the volume will be the same it's going to work out but usually when you see concentration you're dealing with units of marity but because we have a ratio here it could be moles or marity now sometimes you may need to calculate the concentration the moles or the mass of the base or the acid if you need to do that this form of the equation will be helpful so the ratio of Base to acid is equal to 10 ra to the phus pka by the way for buffer solution the pH is equal to the pka whenever you have equal amounts of base and conjugate acid or acid and conjugate base now there's a lot of other formulas in the formula sheet you know if you have situations where you need to calculate the pH of a polyprotic acid like H3 po4 or for aoic ions in water or even if you need to find a pH of an AIC salt so if you want those formulas uh feel free to check out the formula sheet down below now one last thing I'm going to talk about is the quadratic equation because if Ka or KB is not less than 10 to4 you may need to use this so this is the standard form of the quadratic equation once it's in this form if you need to calculate X it's equal to B plus orus the < TK of B ^2 - 4 a c/ 2 a now for those of you who want videos on how to solve difficult problems using this formula in relation to assets and bases or if you just want like a practice test full of questions I'm going to be posting more videos or links to videos in the description section below so feel free to look at that and you can get a ton of examples on how to use these formulas or at least most of these formulas thanks again for watching