For each substance, find the pH from the given hydronium ion conc...

Question

For each substance, find the pH from the given hydronium ion concentration to the nearest tenth. See Example 2(a). grapefruit, 6.3*10^-4

Accepted Answer

Hey, everyone. Here we are asked to evaluate the P H of concrete. If the hydro num ion concentration is given as 4.6 times 10 raised to the power of negative 14. Here we have four answer choice options. Answer A P H is equal to 14.6. Answer B P H is equal to 14.3. Answer C P H is equal to 13. and answer D P H is equal to 13.6. So here, the first step in evaluating the P H of concrete is to recall the P H formula which states that P H is equal to the negative log of the hydro ion concentration, which is H sub 30. So now we just need to substitute in the given value for our concentration into our formula and solve for P H. So our expression becomes P H is equal to the negative log of 4.6 times 10 raised to the power of negative 14. So now our next step is to expand our expression by recalling the logarithmic property which states that the log of A times B is equivalent to the log of A plus the log of B. So now utilizing this formula and comparing it to our expression, we see that our value for A is 4.6 and our value for B is 10 raised to the power of negative 14. So now with these values identified, we can expand our expression as P H is equal to the negative quantity of the log of 4.6 plus the log of 10 raised to the power of negative 14. So now we just want to substitute or distribute in this negative sign into our expression. So we have P H is equal to the negative log of 4.6 minus the log of 10 raised to the power of negative 14. And so now our next step is to expand our expression further. And we see that we can expand our second term which is the log of raised to the power of negative 14. And we can expand this term by recalling the property where we have the log of a raised to the power of X is equivalent to X times the log of A. So now we can compare once again our formula to this term and we see our value for A is 10 and our value for X is negative 14. So now using this formula, we can rewrite our expression as P H is equal to negative log of 4.6 minus negative 14 times log of 10. So now, we can simplify this expression by recalling that the log of 10 is the same as log base 10 of 10. And this expression is simply equivalent to one. So now that we have recalled that the log of 10 is simply just equal to one, we can simplify our expression as P H is equal to the negative log of 4.6 minus negative 14. So now we just want to simplify the signs in our expression. So we have P H is equal to the negative log of 4.6 plus 14. So now our next step is to just evaluate the negative log of 4.6. And so in doing this, we have P H is equal to negative 0.6627 plus 14. Now just adding these terms together, we get 13.3372. And now we just want to round to the nearest 10th. So we see that our P H is equal to 13.3. So with this value for the P H, we are left with answer choice C which tells us that the P H of concrete is 13.3. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

For each substance, find the pH from the given hydronium ion concentration to the nearest tenth. See Example 2(a). grapefruit, 6.3*10^-4

Key Concepts

pH Scale

Hydronium Ion Concentration

Logarithmic Functions

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