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# Definition of pH

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• How can you do this logarithmic calculation in your head- because the MCAT does not allow for calculators? •   Here's an even better explanation: If you see a number that has 1.0 times 10 to an exponent (let's take 1.0 x 10^-4 as an example), the pH is simply the exponent of the power of 10 without the negative sign. So in the example I gave, the pH is 4. You will only get the pH to be the EXACT exponent value ONLY IF you're multiplying by 1.0.

Now, what if the first number isn't 1.0? To give you an idea, take this example: 2.4 x 10^-6. In a case like this, the exponent is 6, but that is NOT your pH! The rule here is that you subtract ONE HALF from the exponent when you have a number other than 1.0 in the mantissa (I believe that's what the position is called?). So we have 6 - 0.5, and you'll have a pH of somewhere between 5.5 and 6.0. Check your answer choices on the MCAT to see what answer falls within that range and you're good to go. The MCAT will NOT have answers looking like 5.5, 5.7, 5.8, etc. They will be more wide spread than that (2.0, 4.3, 5.7, 8.0, etc.). So without even using a calculator, you would select 5.7 out of those answer choices.

Simple, right? Hopefully, this is one of those golden tips whereby if you know what I just stated above, you should never get a pH question wrong on the MCAT....ever.
• Without a calculator follow these steps;
-log(1.5x10^-4)

step 1) divide 1.5 by 10 to get 0.15
step 2) deduct 0.15 from 4 i.e. 4-0.15 = 3.85
Answer on calculator is 3.82 as per video.

Hope this helps. • How do you calculate anti-logs w/out a calculator? I learned how to calculate the pH, but how would you do the anti-logs ? • To find the concentration of H30 or OH, depending on the question, is to take the same basic principle as finding the PH. Looking at the example, he gave in the video of a pH of 3.82 when raising to this power you can immediately see that the answer will be ten raised to the negative 4 (if the pH were 5.21, it would be raised to the negative 6). So you can immediately remove any solution that doesn't have the exponent at -4. As for the answer of 1.51, There is one trick to know. Know that the half way point for pH is at 0.3. So at pH 3.3, the concentration of H3O would be 5.0 x 10^-4. So anything over 0.3 is going to be closer to the exponent value.
• At he states that 3.82 gives you two significant figures. This is incorrect right? Because 3.82 is three sig figs. Shouldn't it just be 3.8 because we only need two sig figs and 3.8 is 2 significant figures. I don't know if this was a mistake or maybe I need to brush up on significant figures but I am pretty sure 3.82 has 3 significant figures. • In logarithmic calculation like this, 3 isn't a significant figure. 3 was originally an exponent. It seemingly looks like a significant figure, but it is not. Exponents are excluded in counting significant figures. In 3,82, the significant figure is just ".82". But if 3.82 is just the case not having an exponent, 3.82 has 3 significant figures.
• Is there any difference in H3O+ or H+? • H⁺ does not actually exist in water because it complexes with water.

So, H⁺ (aq) and H₃O⁺ (aq) are different ways of describing the same thing: the hydronium ion (also called hydroxonium).

In reality H⁺ complexes with more than one molecule of water, but the exact number varies with the conditions of the solution, so it is customary just to depict one molecule of water complexing with the H⁺ ion.
• At , I'm confused as to why he is using the Kw of H2O in order to calculate the [H3O+] for an aqueous NH3 solution. Wouldn't the equilibrium constant for an NH3 solution be different than the Kw for H20 at 25 degrees celsius? • At how should you get the concentration of H3O+ without using a calculator. • for the calculations, can you please help me with scientific calculator? I don't know how to apply looking for the hydroxide ion. like when we have to divide the scienfic notation over a scientific notation to get a scienfic notation. please help. • Are there any examples of solutions with a pH less than 0 or greater than 14? • Isn't it important to distinguish that neutral isn't defined as a pH of 7, rather it's when the concentration of OH- and H3O+ are equal? At he says that because the pH is 11.32 and greater than 7 it's basic, but don't we need to know the temperature and equilibrium constant to really decide what's basic, neutral, or acidic?
(1 vote) • Yes, that is correct. But for the normally encountered laboratory situations, true neutrality does not vary from pH 7 all that much. But for hot water or very cold water the pH of neutral water will vary noticeably from pH 7.

But, at this level of study, we don't usually get into such finer details, which do require more sophisticated mathematical models.

But this goes for any equilibrium constant -- they are all, to varying extents, dependent on temperature. Thus, we have to specify the temperature the K is valid for. If It is not specified, it is assumed to be one of the standard temperatures. For Kw, the standard temperature usually used is 298.15 K.