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^-5

Accepted Answer

Hey, everyone. Here we are asked to categorize the wetland area as a rich fa poor fan or a bog using the provided hydro concentration, which is given as 3.89, multiplied by 10, raised to the power of negative five 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 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, it has a range from 6 to 7.5. Now with a poor fen area, it has a range from 3 to 6. And lastly with a bog, it has a range that is just anything less than three. So now that we have identified the ranges for each type of area, we can move on to solving the problem. And so we first need to recall the formula for the P H, which is that P H is equivalent to the negative log of the hydro ion concentration. So now we just want to substitute in the given information into our formula. 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 five. Now we just want to expand our logarithm as much as possible. So the first step in doing this is applying the product property of logarithms, which will allow us to make this one single logarithm become two individual algorithms. So we have the P H is equal to the negative quantity of log of 3.89 plus the log of 10 raised to the power of negative five. Now we just want to distribute in this negative sign. So we have P H is equal to the negative log of 3.89 minus the log of 10 range to the power of negative five. And now we can expand our second logarithm further, this log of 10 raised to the power of negative five. We can expand this by recalling the power rule for logarithms. So we have P H is equal to the negative log of 3.89 minus negative five multiplied by the log of 10. And now we can simplify this expression further by recalling that the log of 10 is equivalent to one. So simplifying we have P H is equal to the negative log of 3.89 minus negative five. Now we just want to clean up our signs here. Since we have minus a negative, so our expression is P H is equal to negative log of 3.89 plus five. And so now we can see that our logarithm, the log of 3.89 cannot be expanded further. So we just want to find its decimal approximation in doing this, our expression is now negative 0.5899 plus five. And now we just want to sum these two values. And so we get our P H level is 4.4100. And now just rounding to the nearest 10th, we have our P H is just 4.4. And now looking at our ranges for the P H levels for each wetland area, we see 4.4 lies within the range from 3 to 6. So we see that we have a poor wetland area, a poor fen wetland area. So we are left here with answer choice B where again, our area is categorized as a poor fen. 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^-5