At the crack of dawn, the "pH Detective" Alex dives into his daily mission at Sparkling Swims Pool Services. With a hydrogen ion concentration reading of 10^-6 M, what was the pH value of the pool's water this morning?
As with all of these question in this month's challenge, the math and science behind this question are about the level of a senior high school student. So if we recall from high school chemistry class, the formula for calculating pH is a function of ion concentration. It looks like this:
I picked this question for the very first day for a reason. This is a very simple equation. To get the solution in this instance you are simply going to obtain the -Log of 10^-6 (1e-6). This can easily be done on any calculator but there is catch when using a common algebraic calculator. You would have to make sure to use parentheses to separate the -Log and ion concentration reading.
If you forget the parentheses (or you input them incorrectly) in all likelihood the calculator will not produce the correct result. If you don't use parentheses at all, just entering -log 10 ^ -6 might be interpreted as -Log trying to take the negative logarithm of 10, which doesn't make sense in this context. 10 ^ -6 would correctly compute 10e-6, but then it's unclear how this would be combined with -Log.
On most calculators, this would either result in an error or a nonsensical result because the calculator would attempt to compute -Log 10 first, which is not what we want (it would give you -1 since log(10) = 1). Then it would try to raise 10 to the -6, but by then, the operation might not make sense or be combined correctly due to the lack of clear grouping.
With RPN, where parentheses are not required, this is not a problem at all. We can take "bites" out of the equation in the exact same way that we would do it if we were writing this and solving it by hand with a pencil.
It would look like this:
The final result displayed would be 6. The first three steps would place 10e-6 on the x-register of the stack. The LOG function would be acted upon whatever value is in the x-register on the stack (no parentheses and the value can be inputted before the function, which is not typical in most calculators). Lastly, the +/- (change sign) function at the end is how we deal with the negative Log which can seem confusing at first with a typical calculator, but becomes a simple step With RPN. Do you see how similar the motions of the calculator are to solving this equation by hand on your own? I have found that the more I use RPN calculators, the more I find they have in common with how I actually think about and tackle math problems.
In this case the pH level of the pool is 6 which is below the effective concentration (between 7.2 and 7.8). Alex is going to need to add some chlorine to the pool before swimmers begin to arrive. Luckily he had his RPN calculator, so he was able to crunch the numbers quickly and avoid common errors with other calculators, and has plenty of time to fix the issue.
As with all of these question in this month's challenge, the math and science behind this question are about the level of a senior high school student. So if we recall from high school chemistry class, the formula for calculating pH is a function of ion concentration. It looks like this:
I picked this question for the very first day for a reason. This is a very simple equation. To get the solution in this instance you are simply going to obtain the -Log of 10^-6 (1e-6). This can easily be done on any calculator but there is catch when using a common algebraic calculator. You would have to make sure to use parentheses to separate the -Log and ion concentration reading.
If you forget the parentheses (or you input them incorrectly) in all likelihood the calculator will not produce the correct result. If you don't use parentheses at all, just entering -log 10 ^ -6 might be interpreted as -Log trying to take the negative logarithm of 10, which doesn't make sense in this context. 10 ^ -6 would correctly compute 10e-6, but then it's unclear how this would be combined with -Log.
On most calculators, this would either result in an error or a nonsensical result because the calculator would attempt to compute -Log 10 first, which is not what we want (it would give you -1 since log(10) = 1). Then it would try to raise 10 to the -6, but by then, the operation might not make sense or be combined correctly due to the lack of clear grouping.
With RPN, where parentheses are not required, this is not a problem at all. We can take "bites" out of the equation in the exact same way that we would do it if we were writing this and solving it by hand with a pencil.
It would look like this:
1
E
6
+/-
LOG
+/-
The final result displayed would be 6. The first three steps would place 10e-6 on the x-register of the stack. The LOG function would be acted upon whatever value is in the x-register on the stack (no parentheses and the value can be inputted before the function, which is not typical in most calculators). Lastly, the +/- (change sign) function at the end is how we deal with the negative Log which can seem confusing at first with a typical calculator, but becomes a simple step With RPN. Do you see how similar the motions of the calculator are to solving this equation by hand on your own? I have found that the more I use RPN calculators, the more I find they have in common with how I actually think about and tackle math problems.
In this case the pH level of the pool is 6 which is below the effective concentration (between 7.2 and 7.8). Alex is going to need to add some chlorine to the pool before swimmers begin to arrive. Luckily he had his RPN calculator, so he was able to crunch the numbers quickly and avoid common errors with other calculators, and has plenty of time to fix the issue.
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