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Question #44651

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The Question

An analytical chemist is preparing a reaction mixture at $350 \text{ K}$ . Exactly $25.00 \text{ mL}$ of an organic solvent is transferred at $350 \text{ K}$ using a temperature-calibrated Class A volumetric pipette. According to the laboratory's standard operating procedure, the mass must be calculated using the experimentally measured density at the working temperature, which is $1.2 \text{ g/mL}$ . For reference, the literature density of the solvent at $298 \text{ K}$ is $1.275 \text{ g/mL}$ , and its coefficient of thermal volume expansion is $\gamma = 1.10 \times 10^{-3} \text{ K}^{-1}$ .

Calculate the mass of the solvent transferred at $350 \text{ K}$ , reported to the correct number of significant figures.

Options

A.
$3.0 \times 10^1 \text{ g}$
B.
$30.00 \text{ g}$
C.
$30.15 \text{ g}$
D.
$30.05 \text{ g}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Numerical_Precision

Improve calculation stamina and avoid rounding errors in high-stakes competitive examinations.

Concepts Behind This Question

Significant Figures in Arithmetic|Density-Volume-Mass Relationship

Why This Question Is Tricky

Common Mistakes

This problem tests the hierarchy of operations and significant figure rules in arithmetic.

Students are often tempted to use all provided data, falling into the trap of calculating the density at $350 \text{ K}$ using the thermal expansion formula ( $d_{T2} = d_{T1} / (1 + \gamma \Delta T)$ ) to obtain a highly precise density value ( $1.206 \text{ g/mL}$ , leading to $30.15 \text{ g}$ ).

However, the experimental density at $350 \text{ K}$ is already provided with low precision ( $1.2 \text{ g/mL}$ ).

In experimental chemistry, the precision of the final calculated value (mass) is strictly limited by the least precise measurement used in the calculation (density, 2 sig figs), regardless of the high precision of the volumetric glassware (4 sig figs).

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Some Basic Concepts of Chemistry - Class 11 Part 1
Concept	Significant Figures in Arithmetic
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free