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Question

A chemist measures the volume of a solution as 25.34 mL using a burette with a precision of ±0.02 mL.  They then dilute this solution to a final volume of 250.0 mL using a volumetric flask with a precision of ±0.1 mL. What is the absolute uncertainty in the final concentration of the diluted solution?

VENKATESWARARAO · Accepted Answer

## CORE INFORMATION
✓ **Answer**: B
## CONCEPT FRAMEWORK
	**Primary Concept**: Propagation of Uncertainty
	**Related Topics**: Volumetric Analysis, Dilution, Error Analysis
	**Prerequisites**: Basic understanding of uncertainty, dilution calculations
## SOLUTION PATHWAY
**Given Information**:
	Initial volume, V1 = 25.34 mL ± 0.02 mL
	Final volume, V2 = 250.0 mL ± 0.1 mL
	We are looking for the uncertainty in the final concentration.
**Method & Steps**:
	1. Calculate the relative uncertainty of each volume.
		Reasoning: Relative uncertainty is the uncertainty divided by the measured value. This allows us to compare the uncertainties of different measurements.
		Formula/Rule: Relative Uncertainty = Absolute Uncertainty / Measured Value
	2. Calculate the relative uncertainty of V1.
		Working: Relative uncertainty of V1 = 0.02 mL / 25.34 mL = 0.00079
		Key Point: Keep extra decimal places for intermediate calculations.
	3. Calculate the relative uncertainty of V2.
		Working: Relative uncertainty of V2 = 0.1 mL / 250.0 mL = 0.0004
		Key Point:  Keep extra decimal places for intermediate calculations.
	4. Calculate the relative uncertainty in the dilution factor.
		Reasoning: The dilution factor is V2/V1. Since dilution involves division, the relative uncertainties are added to find the relative uncertainty of the dilution factor.  
		Formula/Rule: Relative Uncertainty (division/multiplication) =  Sum of relative uncertainties.
	5. Calculate the combined relative uncertainty.
		Working: Relative Uncertainty (dilution) = 0.00079 + 0.0004 = 0.00119
		Key Point:  This represents the relative uncertainty in the dilution factor and, thus, in the concentration.
	6. Express the uncertainty in terms of the final concentration.
		Result: The uncertainty in the final concentration is 0.00119 times the final concentration. This can be rounded to 0.0012 times the final concentration.
		Verification: The answer is a relative uncertainty, so it should be a dimensionless number or be expressed as a proportion.
 ## OPTION ANALYSIS
[A] :x: This option is not the uncertainty of the final concentration. It is not a relative uncertainty or a proportion of the final concentration. Thus incorrect.
[B] ✓: The calculation shows that the relative uncertainty is approximately 0.0012, meaning the final concentration has an uncertainty of 0.0012 times itself.
[C] :x: This option is not the uncertainty of the final concentration. It is not a relative uncertainty or a proportion of the final concentration. Thus incorrect.
[D] :x: This option is not the uncertainty of the final concentration. It is not a relative uncertainty or a proportion of the final concentration. Thus incorrect.
 ## LEARNING AIDS
	**Common Mistakes**:
		1.[Error 1]: Forgetting to use relative uncertainty when multiplying or dividing quantities. It is incorrect to simply add absolute uncertainties directly in these cases.
		2.[Error 2]: Rounding too early in calculations. Keep extra digits in intermediate calculations to avoid introducing rounding errors in the final result.
	**Quick Tips**:
		1.[Helpful shortcut]: When dividing or multiplying, you add relative uncertainties. When adding or subtracting, you add absolute uncertainties.
		2.[Memory aid]: Think of relative uncertainty as the 'percentage error' expressed as a decimal.

VENKATESWARARAO · Answer

0.000012 M

VENKATESWARARAO · Answer

The correct Option is "0.0012 times the final concentration"

VENKATESWARARAO · Answer

0.002 M

VENKATESWARARAO · Answer

0.00012 M

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