How would I do Dimensional Analysis in Chemistry?
1. 261g --------> kg
2. 3 days ---------> seconds
3. 9, 474 mm--------> cm
Is there a certain method to do each one? Please help I am confused on this.
There is a method and it works every time. Here is the first one with way too much explanation but I want you to understand.
You want g to kg. Copy down the conversion factor.
1000 g = 1 kg. There are two ways to write this. The two ways to write these factors are
1000 g/1 kg or 1 kg/1000 g. You will use one of these two to make the conversion.
We write 261 g x factor = ? kg. So all you need to do is to figure out which of those two factors above you want to use. It should be obvious that you have a 50% chance if you just guess. But we want to do it so you never guess and you ALWAYS get it right. The secret is in the units. You want to make the units come out right.
261 grams x factor = ? kg
I could write this one of two ways.
261 grams x (1000 g/kg) = ? kg or
261 grams x (1 kg/1000 g) = kg. Which one do we use? Look at the units.
The top one gives you grams x grams/kg = kg which isn't true.
The lower one gives you grams*kg/grams = kg which is true. So we know to use the lower one That will be
261 g x (1 kg/1000 g) = 0.261 g.
I know the first question you will ask is why is it so long? Partly because I'm long winded. But you will soon catch on that the numerator of the first term must cancel with the denominator of the factor and the numerator of the factor is always the unit you want in the answer.
I'll do the 3 days to seconds in one line so you can see how it works.
3 days x (24 hr/day) x (60 min/hr) x (60 sec/min) = ? seconds.
You see the days cancel to give hours, then hr cancels to give min, then min cancel to give seconds. Easy when you get the hang of it. I'll leave the last one for you. I'll check you answer if you will post it but it's past my bed time now. I'll check it tomorrow.
Good morning. I greatly appreciate you explaining this a bit more to me because I am completely lost. Let me ask you this. When I have written.
3 days----------> seconds
So just like in the first problem of the 261g---------> to kg do you have to look up each conversion seperately to figure this out. How would you know whether you have to look grams to kg or do you always just look what is 1 kg to gram?
So for instance #2. like you gave me the example do I just have to look seconds to day and then determine the conversation rate? I will try number 3 on my own and see if I have the hang of it a bit.
I truly appreciate your explanation because when you don't know where to start and on top of that I am not very good at math it's somewhat hard.
Good morning so with the 3rd problem.
9, 474 mm------->cm
I see more clearly how you said with the very first problem of how it cancels out. But not sure how you figure it out sideways. Fraction form of writing seems simple.
My answer on this one is:
947.4cm
So what I did is as follows:
I had to look up cm to just millimeter and I found that 1 cm=10 millimeters
9, 474mm/1 x 1cm/10mm but written as a fraction on both sides.
Then I canceled out the mm on the left and canceled out the mm on the right which left me with cm.
Then I took 9, 474 divided by 10=947.4
947.4 is my answer to this one.
I may have to go back and review with you #3 a bit later.
Let me take these one at a time. Your answer for 3 is correct. And you looked up cm to mm properly and found 1 cm = 10 mm so that's your factor. The complete equation is 9,474 mm x (1 cm/10 mm) = 947.4 cm.
About days to seconds. IF you have a table that gives you 1 day = 86,400 seconds then you can do the factor business in 1 step. It would be written as 3 days x (86,400 seconds/1 day) = ? seconds. But there aren't many people in this world that knows what that factor is. I didn't know it either and I looked it up. So if you don't know the factor and you can't find it anywhere you go to plan B. I have found in my career that it's good to know SOME conversion factors. So if I have days to seconds I can think it through and I say OK. I have a day, I can convert to hours, then minutes, then to seconds so that is 3 conversions and you don't need to go through the steps as I did in the first problem we did. You can write them in all at once and that's what I did. For the first question about g to kg, any table that has g to kg or kg to g will work. You might find a table that says 1000 g = 1 kg or it might say 1 kg = 1000 g or it could say 1 g = 0.001 kg. As long as you have the two units your set. We can prove that this way. Remember we had 261 g = 0.261 kg when we used the 1000 g = 1 kg factor. But the 1 g = 0.001 kg factor works the same like this. 261 g x (0.001 kg/1 g) = 0.261 kg. We get the same answer. The grams unit cancels leaving the unit of kg which is what we want in the answer.
Keep up the good work. Don't be intimidated by math or chemistry. You just follow the rules and think each problem through. The secret word here is "think".
Yes, there is a method called dimensional analysis that you can use to convert between different units in chemistry. The technique involves setting up conversion factors using conversion factors or unit ratios. Let's go through each conversion step by step:
1. To convert from grams (g) to kilograms (kg), you need to know the conversion factor between these two units. Since there are 1000 grams in one kilogram, the conversion factor is 1000 g/1 kg. Now, to set up the dimensional analysis equation, write down the given value (261g) and multiply it by the conversion factor in such a way that the grams cancel out and you are left with kilograms. Here's how it looks:
261g * (1 kg/1000 g) = 0.261 kg
So, 261 grams is equal to 0.261 kilograms.
2. To convert from days to seconds, you need to know the conversion factor. There are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute. Therefore, the conversion factor is:
1 day * (24 hours/1 day) * (60 minutes/1 hour) * (60 seconds/1 minute) = 86,400 seconds
To set up the equation, write down the given value (3 days) and multiply it by the conversion factor in such a way that the days cancel out and you are left with seconds:
3 days * (86,400 seconds/1 day) = 259,200 seconds
So, 3 days is equal to 259,200 seconds.
3. To convert from millimeters (mm) to centimeters (cm), you need to know the conversion factor. Since there are 10 millimeters in one centimeter, the conversion factor is 10 mm/1 cm.
With this conversion factor, set up the equation as follows:
9,474 mm * (1 cm/10 mm) = 947.4 cm
So, 9,474 millimeters is equal to 947.4 centimeters.
In all three cases, the dimensional analysis technique involves setting up the appropriate conversion factors using fractions and canceling out the units until you arrive at the desired unit.