Do I have enough information to solve this density problem?

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Discussion Overview

The discussion revolves around a homework problem involving the volume of ice formed from water when frozen at -10 degrees Celsius. Participants explore the implications of density changes during the phase transition from water to ice, and whether sufficient information is provided to solve the problem.

Discussion Character

  • Homework-related
  • Debate/contested
  • Exploratory

Main Points Raised

  • One participant expresses uncertainty about needing the mass of the water or its density to proceed with the calculations.
  • Another participant critiques the clarity of the problem, suggesting it assumes the bottle can expand or will break, leading to confusion about the conditions of the problem.
  • Some participants assert that the mass of water remains constant during freezing, but there is disagreement about how to determine this mass from the given information.
  • There is confusion regarding the temperature of the ice, with participants noting a potential typo in the problem statement that lists the density of ice at 10 degrees Celsius, which raises questions about the physical feasibility of the scenario.
  • One participant calculates the mass of water based on its density at 25 degrees Celsius and proposes a method to find the volume of ice using the density of ice.
  • Another participant reminds others to consider significant figures in their calculations.

Areas of Agreement / Disagreement

Participants generally disagree on whether the problem provides enough information to solve it, with some asserting that it does while others express confusion and uncertainty regarding the conditions and assumptions involved.

Contextual Notes

There are unresolved issues regarding the temperature at which the ice is said to exist and the implications of density changes during the phase transition. The problem statement may contain a typo that affects the discussion.

Eclair_de_XII
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Homework Statement


"If a soft-drink bottle whose volume is 1.50 L is completely filled with water and then frozen to -10 degrees Celsius, what volume does the ice occupy? Water has a density of 0.997 g/cm^3 at 25 degrees Celsius; ice has a density of 0.917 g/cm^3 at -10 degrees Celsius."

Homework Equations


D = m/V
D = m/1500 mL
m = x(0.997) + y(0.917)
x + y = 1500 mL
x = 1500 - y

The Attempt at a Solution


m = (1500 - y)(0.997) + y(0.917)
m = 1495.5 - y0.997 + y0.917
m = 1495.5 - y0.08

I feel like I would need the mass of the bottle's contents or its density in order to proceed. Am I plugging in my numbers wrong?
 
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Question is rather lousy if you ask me. I guess they want you to assume bottle is either elastic enough to expand, or it simply breaks (and all water is converted to ice).
 
I agree; my chemistry professor doesn't seem to know what she's talking about.

But do I have enough information to solve for the volume of the ice?
 
Yes. Mass of water doesn't change.
 
But I don't know what the mass of the water is...
 
You have enough data to calculate it.
 
Eclair_de_XII said:
But I don't know what the mass of the water is...

Re-read the problem statement carefully:

"If a soft-drink bottle whose volume is 1.50 L is completely filled with water and then frozen to -10 degrees Celsius, what volume does the ice occupy? Water has a density of 0.997 g/cm^3 at 25 degrees Celsius; ice has a density of 0.917 g/cm^3 at 10 degrees Celsius."

Some problems will not spoon-feed you all the data you need for solution. You have to do a little work to find it.

It's not clear how the ice exists at a temperature of 10 degrees Celsius, unless this is a typo which occurred when copying the problem statement.
 
If that's the case, then wouldn't the ice take up the whole bottle since it can't be two different temperatures?
 
Eclair_de_XII said:
If that's the case, then wouldn't the ice take up the whole bottle since it can't be two different temperatures?
That wasn't the point I was trying to make, but now that you asked it ...

What happens to ice when the temperature is greater than 0 degrees Celsius?

(Hint: What is the freezing point of water?)
 
  • #10
The freezing point of water is 0 degrees Celsius, isn't it?

If it's greater, then it starts to melt?
 
  • #11
Eclair_de_XII said:
The freezing point of water is 0 degrees Celsius, isn't it?

If it's greater, then it starts to melt?
Yes. So the density of ice at 10 degrees Celsius seems to cover an impossible situation.
 
  • #12
SteamKing said:
It's not clear how the ice exists at a temperature of 10 degrees Celsius, unless this is a typo which occurred when copying the problem statement.

I'm sorry for not pointing this out earlier, but this is correct.
 
  • #13
Eclair_de_XII said:
If that's the case, then wouldn't the ice take up the whole bottle since it can't be two different temperatures?

Please reread my first post in the thread. Final volume of the ice is not 1.5L.
 
  • #14
Okay, 1.50 L of water (at 25 degrees Celsius) is poured into water. It has a mass of m = 1500(0.997) = 1495.5 g. This mass does not change, even when the water is frozen. However, its volume of the water does change as it turns to ice? Given that the density of ice is 0.917 g/mL, I can calculate the volume from that and the mass.

m = 1495.5
1495.5 = V(0.917)
V = 1495.5/0.917
V = 1630.862 mL
 
  • #15
And that would be my approach to solving the question.

Watch your significant figures.
 
  • #16
Okay, thanks.
 

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