yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Worked example: Calculating concentration using the Beer–Lambert law | AP Chemistry | Khan Academy


2m read
·Nov 10, 2024

So I have a question here from the Cots, Trickle, and Townsend Chemistry and Chemical Reactivity book, and I got their permission to do this. It says a solution of potassium permanganate has an absorbance of 0.53 when measured at 540 nanometers in a 1 centimer cell. What is the concentration? What is the concentration of the potassium permanganate?

Prior to determining the absorbance for the unknown solution, the following calibration data were collected for the spectrophotometer. The way that we would tackle this is we know that there is a linear relationship between absorbance and concentration. We could describe it something like this: that absorbance is going to be equal to some slope times our concentration, and you could say some y-intercept.

If we're purist about it, then the y-intercept should be zero because at a zero concentration, you should have a zero absorbance. But the way that chemists would typically do it is that they would put these points into a computer and then have the computer do a linear regression. You could also do that by hand, but that's a little bit out of the scope of this video.

I did that; I went to Desmos and I typed in the numbers that they gave, and this is what I got. So I just typed in these numbers, and then it fit a linear regression line to it, and it got these parameters: m is equal to this, and b is equal to this.

Now we could say significant figures; it seems like the small significant figures here we have are three, but we could just view the m and the b as intermediate numbers in our calculations. So what I'm going to do is I'm going to use this m and b, and then my final answer I'm going to round to three significant figures.

So what this tells us is that our absorbance is going to be 5.65333 times our concentration minus 0.008. Now they've given us what a is. Let me get rid of all of this stuff here. They told us that our absorbance is 0.539. So we know that 0.539 is equal to 5.65333c minus 0.0086.

And then if you want to solve for c, let's see. We could add this to both sides first, so you get 0.539 plus 0.0086 is equal to 5.65333c. Then divide both sides by this, and you would get c is equal to, or is going to be approximately equal to—be a little careful; all of these would really be approximates.

c is going to be approximately equal to 0.539 plus 0.0086 divided by 5.65333. Of course, we want to round to three significant figures. All right. 0.539 plus 0.0086 is equal to that divided by 5.65333 is equal to this.

So if we go three significant figures, this is going to be 0.0969. So I would write the concentration is approximately 0.0969 molar.

More Articles

View All
Metaverse: Beyond Human
Imagine a world where you wake up, head to the office in the morning, to a party with friends in the evening, and then a live concert at midnight, all while sitting in the warmth of your home or from the comfort of your bed. That might just be part of hum…
How I was held at gunpoint while selling a private jet!
The first jet I ever sold in my life, I was held at gunpoint 3 ft away from me. It’s a long story. So, the first time I sold the jet, I was 23 years old. I flew to America, to North Carolina. We were signing a deal with a Venezuelan buyer; he had two of h…
After the Avalanche: Life as an Adventure Photographer With PTSD (Part 2) | Nat Geo Live
In the field, I feel so connected to everything, but then I’d come home and I would feel so disconnected, and I started to hate coming home because I wasn’t stimulated. I’d have to sit in this quietness and feel this pain, and I didn’t know where it was c…
If you can't focus, please watch this video…
Do you know why your brain is like a browser with too many tabs open? What if I told you that you’re just one funny cat video away from losing your focus completely? In this video, I will dive into a major culprit of focus. By the end of this video, you’l…
Albatrosses' Life-Long Bond Begins With Elaborate Courtship – Ep. 3 | Wildlife: Resurrection Island
You think that’s fighting? The biggest bird in the world would be quite straightforward. Turns out, no! Here he comes. [Music] That is the biggest bird on the planet. Each one of those wings is as wide as I am tall. The wandering albatross’s wingspan is o…
Freedom According to the Declaration Of Independence | The Story of Us
I’m headed to the American Philosophical Society in Philadelphia to meet with its librarian Patrick Spiro. He studies documents dating back to the time of the country’s founding. What you’re looking at here is one of the first printings of the Declaration…