Solutions 6

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Christian Lawson-Perfect

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Christian Lawson-Perfect 7 years, 2 months ago

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Question statement

Answer the following question. Please enter your answer as a decimal, not a fraction. Give your answer to 3 decimal places.

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			Name	Type	Generated Value

final_volume	integer	200
stock_volume_used	integer	50
stock_molarity	number	0.2
final_molarity	number	0.05
final_concentration	number	50

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
100 * random(2..5)

JME function reference

Description

Volume of solution after dilution.

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

200

This variable doesn't seem to be used anywhere.

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A solution of glucose was prepared by diluting $\var{stock_volume_used}$ ml of the "stock" glucose solution to $\var{final_volume}$ ml. The concentration of glucose in the final solution was $\var{final_concentration}$ mM. What was the concentration of glucose in the "stock" solution in M (mol/L)?

Unnamed gap M

Advice

Solution:

First, we convert $\var{final_volume}$ ml to a volume in litres. There are 1000ml in 1L so $\var{final_volume}$ ml is equal to

$\dfrac{\var{final_volume}}{1000} = \var{final_volume / 1000} \text{ L.}$

Next, we can calculate how many mmol of glucose there are in the final solution. The formula for this is

$\text{volume of liquid (in litres)} \times \text{concentration (in mmol/L)} = \text{number of millimoles of substance}$ .

[Note: This is slightly different to the formula on the wiki page for molar calculations. This is because we are currently working with mmol and mM as opposed to mol and M. If you prefer, you can first convert all values in mmol and mM to values in mol and M respectively and use the formulas as given on the wiki page. If you would like to read a little more about converting between units, see the wiki page on dimensions in the animal science section.]

Putting in our numbers we find that there are

$\var{final_volume / 1000} \times \var{final_concentration} = \var{(final_volume / 1000) * final_concentration} \text{ mmol}$

of glucose in the final solution.

We also need to convert $\var{stock_volume_used}$ ml to a volume in litres. $\var{stock_volume_used}$ ml is equal to

$\dfrac{\var{stock_volume_used}}{1000} = \var{stock_volume_used / 1000} \text{ L}.$

We didn't add any more glucose when diluting the "stock" solution so the "stock" solution also contained $\var{(final_volume / 1000) * final_concentration}$ mmol of glucose in $\var{stock_volume_used / 1000}$ L of solution. We calculate the concentration of the "stock" solution in mM (mmol/L) using the formula

$\dfrac{\text{number of millimoles of substance}}{\text{volume of liquid (in litres)}} = \text{concentration (in mmol/L)}$ .

[Again, if you prefer, you can convert the amount of substance in mmol to an amount in mol before doing the calculation and use the formulas as given on the wiki page.]

Putting in our numbers, we find that theconcentration of the "stock" stock in mM is

$\dfrac{\var{(final_volume / 1000) * final_concentration}}{\var{stock_volume_used / 1000}} = \var{stock_molarity * 1000} \text{ mM}.$

Finally, we have been asked to give the answer in M so we have to convert $\var{stock_molarity * 1000}$ mM to a concentration in M. There are 1000mM in 1M so the concentration of the "stock" solution in M is

$\begin{align}\dfrac{\var{stock_molarity * 1000}}{1000} & = \var{stock_molarity}\text{ M} \\ & = \var{precround(stock_molarity, 3)} \text{ M to 3 d.p.} \end{align}$

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Taxonomy: mathcentre

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Christian Lawson-Perfect 7 years, 2 months ago

Christian Lawson-Perfect 10 years, 1 month ago

Jamie Antoun 10 years, 10 months ago

Error in variable testing condition

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Generated value: `integer`

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Solutions 6

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 7 years, 2 months ago

Christian Lawson-Perfect 10 years, 1 month ago

Jamie Antoun 10 years, 10 months ago

Error in variable testing condition

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Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`