Simplified 2.0 mL .20M X added to 9ml

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Discussion Overview

The discussion revolves around calculating the concentration of a solution after mixing 2.0 mL of a 0.20 M solution of "X" with 9 mL of another solution, resulting in an 11 mL total volume. Participants explore the correct application of molarity and the calculations involved in determining the final concentration of "X".

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant calculates the concentration of "X" as 0.0363636... M based on the formula M = moles/liters, using 2.0 mL of 0.20 M to find 0.0004 moles and dividing by the total volume of 0.011 L.
  • Another participant suggests that the initial calculation is incorrect, pointing out that the notation used implies an equality that is misleading.
  • Some participants clarify that 2.0 mL is equivalent to 0.002 L, and thus 0.002 L of 0.20 M "X" indeed equals 0.0004 moles.
  • There is a discussion about the importance of clear notation and the implications of using equality signs in calculations.
  • One participant notes that while the calculated concentration of 0.036 M is correct, it is important to remember that volumes may not always be additive.

Areas of Agreement / Disagreement

Participants express differing views on the clarity of the notation used in the calculations, with some agreeing on the final concentration while others challenge the initial presentation of the calculations. The discussion remains unresolved regarding the best practices for notation and clarity in mathematical expressions.

Contextual Notes

There are unresolved issues regarding the assumptions made about volume additivity in solution mixing, as well as the clarity of mathematical notation used in the calculations.

Whalstib
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Simplified... 2.0 mL .20M "X" added to 9ml

Homework Statement



Simplified...

2.0 mL .20M "X" added to 9ml making an 11mL soln.

What would be the concentration of "X"?

Homework Equations



M= molarity=moles/liters

The Attempt at a Solution



2.0ml=.002L x .2M= .0004 moles/.011L=.0363636...M "X"

Right?...

Thanks,

Warren
 
Last edited:
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Whalstib said:

Homework Statement



Simplified...

2.0 mL .20M "X" added to 9ml making an 11mL soln.

What would be the concentration of "X"?


Homework Equations



M= molarity=moles/liters



The Attempt at a Solution



2.0ml=.002L x .2M= .004 moles/.011L=.363636...M "X"

Right?...

Thanks,

Warren

Sure about that? :smile:
 


Now I am...

.0363636...
 


Whalstib said:
2.0ml=.002L x .2M= .0004 moles/.011L=.0363636...M "X"

It suggests correct thinking, but writing 2 mL=0.0004 moles and asking if it is correct is... funny. It is about as correct as writing

2=7

5=3.14

and so on.

Compare dilution and mixing calculations.
 


Molarity = moles/liters so to revert to moles i would multiply by liters...
.2M x .002 liters = .0004 moles

Is this the problem?

Mr. Borek, where is it stated .2ml = .0004 moles?

Let's re establish the idea:

.002L of .2M "X" would by definition = .0004 moles "X" ... right?
The .0004 moles "X" are added to "Y" to create a .011L soln creating a .0004/.011 (moles/liter=molarity) = .0363636...M "X"... right?

Since I've been confused by the above responses could some one confirm or deny my results and suggest a formula to obtain the correct one if I am wrong?

Thanks,

Whalstib
 
Last edited:


Whalstib said:
Molarity = moles/liters so to revert to moles i would multiply by liters...
.2M x .002 liters = .0004 moles

Is this the problem?

Borek was commenting on the way you set out your working, not the actual math and chemistry involved.

If your first line was "2.0ml=.002L", then it would be ok; but you instead had "2.0ml=.002L x .2M". 2mL is indeed equivalent to 0.002L, but it is not the same thing as 0.0004 moles. If you ever use an equality sign in your working, you should make sure that the quantities on either side have the same dimensions.

If i was doing this problem, i'd break it into multiple lines:
2mL = 0.002L
0.002L * 0.2 mol/L = 0.0004 moles of X
0.0004 moles / 0.011L = 0.03636 mol/L

Or something similar.

EDIT: I must have posted this just after you edited the post above.
 


Whalstib said:
Mr. Borek, where is it stated .2ml = .0004 moles?

My fault with not quoting you exactly, but you started with

Whalstib said:
2.0ml=.002L x .2M

Which is equivalent of stating 2mL=0.0004 mole. That's an obvious shortcut, and notation is awkward - it suggests something you don't mean.

Whalstib said:
.002L of .2M "X" would by definition = .0004 moles "X" ... right?
The .0004 moles "X" are added to "Y" to create a .011L soln creating a .0004/.011 (moles/liter=molarity) = .0363636...M "X"... right?

0.036M is a correct result. And theory behind (which is not different from what you did) is on the page I linked to.

Note that volumes are not additive, so in general it may happen that 2mL + 9mL are not 11 mL. Unlikely in the case of diluted solutions, and rarely worth of taking into account, but it may hit one day if you ignore it.

--
methods
 


Thanks!

Sorry for the sloppy notation.

I'll try to work on that as I have LOTS of questions this semester!

Whalstib
 

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