Relative Density of Glycerin: 66 kg / 1000kg/m3 = 0.066

In summary, the conversation was about calculating the relative density of glycerine based on the given data of the mass of a receptacle when empty, filled with water, and filled with glycerin. The formula for relative density was discussed and it was determined that the ratio of the densities of glycerin and water is equal to the ratio of their masses when they occupy equal volumes. The correct answer for the relative density of glycerin was found to be 1.260.
  • #1
Nanu Nana
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A receptacle has a mass of 3 kg when it is empty, 53 kg when it is filled with water, and 66 kg when it is filled with glycerin. Calculate the relative density of glycerine.
I know the formula to find out the relative density.
d= absolute density / reference density ( 1000kg/m3)
 
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  • #2
What do the data tell you about the mass and volume of each liquid?

You say ##Relative\ Density_x= \frac{density_x}{reference\ density}##
Do you know another formula for density, relating it to mass and volume?
Can you use that and your data to substitute into your RD formula?
 
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  • #3
Merlin3189 said:
What do the data tell you about the mass and volume of each liquid?

You say ##Relative\ Density_x= \frac{density_x}{reference\ density}##
Do you know another formula for density, relating it to mass and volume?
Can you use that and your data to substitute into your RD formula?

Density is mass / volume but the volume is not given.
 
  • #4
But the receptacle has a certain volume, even if you don't know what it is. Just use a symbol for it, like v.
 
  • #5
Also, why is the reference density 1000kg/m3?
 
  • #6
Merlin3189 said:
But the receptacle has a certain volume, even if you don't know what it is. Just use a symbol for it, like v.

Ok so : relative density = 66kg/ v / 1000 kg/ m3 ?
 
  • #7
Merlin3189 said:
Also, why is the reference density 1000kg/m3?
Because it is filled with water. And the reference for water is 1000kg/ m3? or Am I wrong ?
 
  • #8
Ok. So the 1000 kg/m3 is not helpful here. You have some more info in the data.
 
  • #9
Merlin3189 said:
Ok. So the 1000 kg/m3 is not helpful here. You have some more info in the data.
I didn't leave out any info . I just copied what was written on my textbook
 
  • #10
Your receptacle has volume = ? It holds mass of glycerin = ? It holds mass of water = ?
Then, from your data, density of glycerin = ? and density of water = ?
 
  • #11
Merlin3189 said:
Your receptacle has volume = ? It holds mass of glycerin = ? It holds mass of water = ?
Then, from your data, density of glycerin = ? and density of water = ?
Sorry I don't understand :(
 
  • #12
Given: receptacle mass = 3 kg (empty), 53 kg filled with water, 66 kg filled with glycerin
So: receptacle volume = v , water volume = v, glycerin volume = v
and water mass = ? , glycerin mass = ?
So density of water = ? and density of glycerin = ?
Finally RDglycerin = (density of glycerin) / (density of water) = ? / ? = ?
 
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  • #13
Merlin3189 said:
Given: receptacle mass = 3 kg (empty), 53 kg filled with water, 66 kg filled with glycerin
So: receptacle volume = v , water volume = v, glycerin volume = v
and water mass = ? , glycerin mass = ?
So density of water = ? and density of glycerin = ?
Finally RDglycerin = (density of glycerin) / (density of water) = ? / ? = ?
mass water = 53-3 =50 kg water, mass glycerin = 66-3-53 = 10 kg
density of water = 50kg / v density of glycerin = 10kg/ v
 
  • #14
mass glycerin = 66-3-53 is not correct.
Mass of water = mass of container full of water - mass of container = 53 - 3 = 50 kg
Mass of glycerin = mass of container full of glycerin ...
 
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  • #15
Merlin3189 said:
mass glycerin = 66-3-53 is not correct.
Mass of water = mass of container full of water - mass of container = 53 - 3 = 50 kg
Mass of glycerin = mass of container full of glycerin ...
mass of glycerin = 66 kg-3kg =63 kg glycerin
 
  • #16
So now density of glycerin ##= \frac{63}{v}## and density of water ##= \frac{50}{v}## and you can work out RD = density G / density W
 
  • #17
Merlin3189 said:
So now density of glycerin ##= \frac{63}{v}## and density of water ##= \frac{50}{v}## and you can work out RD = density G / density W

Now I get . Thank you very much sir !

d= 63v/50v = 1.260
 
  • #18
Not quite! You got the right idea, but 63/50 is less than 2

##RD_g =\frac {density_g}{density_w} = \frac{\frac{63}{v}}{\frac{50}{v}}=\frac{63}{50}=##
 
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  • #19
Merlin3189 said:
Not quite! You got the right idea, but 63/50 is less than 2

##RD_g =\frac {density_g}{density_w} = \frac{\frac{63}{v}}{\frac{50}{v}}=\frac{63}{50}=##
Yes sorry it was mistake. I did have 1.260 as answer but i mistyped it . Thank you very much. And sorry it took quite long for me to understand
 
  • #20
Oops! I obviously typed that last post wrongly as well. Anyhow ..
That was a long way round to get there. The crucial thing about this question is that you have equal volumes of the two liquids.
So the ratio of the densities is the same as the ratio of the masses.
$$ RD_x = \frac {mass_x}{mass_w}$$ where massx and massw are for equal volumes.
PS. It doesn't matter taking time, so long as you understand in the end. On PF I can't just tell you an answer, I have to try to lead you to it.
 
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  • #21
Merlin3189 said:
Oops! I obviously typed that last post wrongly as well. Anyhow ..
That was a long way round to get there. The crucial thing about this question is that you have equal volumes of the two liquids.
So the ratio of the densities is the same as the ratio of the masses.
$$ RD_x = \frac {mass_x}{mass_w}$$ where massx and massw are for equal volumes.
PS. It doesn't matter taking time, so long as you understand in the end. On PF I can't just tell you an answer, I have to try to lead you to it.
I was wondering why you didn't gave me correct answer right away . But u did a good thing. I understand it better now .
 
  • #22
Nanu Nana said:
I was wondering why you didn't gave me correct answer right away . But u did a good thing. I understand it better now .

He is not allowed to do that; it is very much against the PF Rules. Those rules are there precisely so you can make a statement like in your last sentence above!
 
  • #23
Ray Vickson said:
He is not allowed to do that; it is very much against the PF Rules. Those rules are there precisely so you can make a statement like in your last sentence above!

Oh Sorry I didn't know .Thank you for informing me
 

What is relative density?

Relative density, also known as specific gravity, is the ratio of the density of a substance to the density of a reference substance at a specific temperature and pressure.

How is relative density of a substance measured?

Relative density is typically measured by comparing the weight of a given volume of the substance to the weight of the same volume of water at the same temperature and pressure.

What is the relative density of glycerin?

The relative density of glycerin is 0.066, meaning that it is 0.066 times as dense as water.

What is the significance of the relative density of glycerin?

The relative density of a substance can provide information about its composition, purity, and potential uses. In the case of glycerin, its low relative density makes it useful in a variety of industries, such as cosmetics and food production.

How does the relative density of glycerin compare to other substances?

The relative density of glycerin is relatively low compared to other substances, such as iron (7.87) and gold (19.32). However, it is higher than some other liquids, such as ethanol (0.789) and gasoline (0.71).

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