Suppose that water from a wetland area is sampled and found to ha...

Question

Suppose that water from a wetland area is sampled and found to have the given hydronium ion concentration. Determine whether the wetland is a rich fen, a poor fen, or a bog. See Example 3. 2.49*10^-7

Accepted Answer

Hey, everyone. Here we are asked to categorize the wetland area as a rich fen, a poor fen or a bog using the provided hydro concentration, which is given as 3.89, multiplied by 10, raised to the power of negative seven in moles per liter. Here we have four answer, choice options, answer choice. A rich F answer B porn answer C fog or answer D none of these. So before we can begin solving this problem, we first need to recall the P H ranges for each type of wetland area. So beginning with the rich fen wetland area, we know that the P H level is between six and 7.5. And now for the poor fen, the range is from 3 to 6. And lastly for a bog, the range is always going to be less than three. So now beginning to solve this problem, we now need to recall the formula for the P H, which is that the P H is equivalent to the negative log of the hydro num ion concentration. So now we just want to substitute in the given information into our formula. So we have the equation P H is equal to the negative log of the given value, which is 3.89, multiplied by 10 raised to the power of negative seven. So now to find the value of the P H, we want to expand our logarithm as much as possible. So the first expansion we can make here is by recalling the product property of logarithms, which allows us to expand this one logarithm to two logarithms. So we have P H is equal to the negative quantity of log of 3. plus the log of 10 raised to the power of negative seven. Now we just want to distribute in the negative sign. So we have P H is equal to the negative log of 3.89 minus the log of 10 raised to the power of negative seven. So now focusing further on the log of 10 raised to the power of negative seven, we can expand this logarithm by recalling the product or the power property of logarithms. And so we have P H is equal to the negative log of 3.89 minus negative seven multiplied by the log of 10. And now we know we can simplify the log of 10 because we know log of 10 is equivalent to one. So just simplifying our equation, we have P H is equal to the negative log of 3.89 minus negative seven. Now just cleaning up the signs here, we have P H is equal to the negative log of 3.89 plus seven. And now we cannot expand the negative log of 3.89 any further. So we want to go ahead and find its decimal approximation. And so with its decimal approximation, we have the equation now as negative 0.5899 plus seven. And now just summing these two values, we find that our P H is 6.4100. And now we just want to round to the nearest 10th. So we find that our P H level is 6.4. And since we see that this 6.4 is within the range from 6 to 7.5, we know that we have a rich fen wetland area. So we are left here with answer choice. A where again, we have a rich ben wetland area. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

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Suppose that water from a wetland area is sampled and found to have the given hydronium ion concentration. Determine whether the wetland is a rich fen, a poor fen, or a bog. See Example 3. 2.49*10^-7

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