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^-2

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 three in moles per liter. Here we have four answer, choice options, answer choice, a rich fun answer B poor fun answer C bog or answer D none of these. So to begin this problem before we can actually solve it, we first need to recall the P H ranges for each type of wetland area. So beginning with the rich fen wetland area, it has a P H range from 6 to 7.5. Now moving on to a poor, it has a P H range from 3 to 6. And lastly, a bog has a P H range that is less than three. So now we can start solving the problem. And we first want to recall the formula for the P H which states that the P H is equivalent to the negative log of the hydro ion concentration. So now we just want to substitute in the given information. So we have 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 three. And now we just want to manipulate this equation so that we expand the logarithms as much as possible. And now the first expansion we can make involves the product property. So in using the product property for logarithms, we have P H is equal to the negative log of 3.89 plus the log of 10 raised to the power of negative three. And now we just want to distribute in the negative sign. So our equation is now P H is equal to the negative log of 3.89 minus the log of 10 rings to the power of negative three. So now just focusing on the log of 10 raised to the power of negative three, we can expand this logarithm further by recalling the power rule for logarithms. And with the power rule, our equation becomes P H is equal to the negative log of 3.89 minus negative three, multiplied by the log of 10. And now we can simplify the second logarithm further by recalling that the log of 10 is equivalent to one. So just simplifying, we have P H is equal to the negative log of 3.89 minus negative three. Now just cleaning up our science here, since we have minus negative three, we actually have P H is equal to the negative log of 3.89 plus three. And now, since we cannot expand our logarithm any further, we can just find its decimal approximation. So we have P H is equal to negative 0.5899 plus three. Now just summing these two values, we get that the P H is equal to 2.4100. Now just rounding to the nearest 10th, we have P H is equal to 2.4. And now looking at our ranges for each type of wetland area, we see that 2.4 is less than three. And therefore, we know that we have a bog wetland area. So we are left here with answer choice C where again, the wetland area is categorized as a bog. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Struggling with College Algebra?

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^-2

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