Examkin

Question

Difficulty: MediumTranslating Data Formats

A laboratory experiment measured the rate of thermal decomposition (in mmol/L⋅s\text{mmol/L}\cdot\text{s}) of four organic compounds (Compounds W, X, Y, and Z) across three temperatures (TT, in K\text{K}). The results are shown in the table below:

CompoundRate at 300 K300\text{ K}Rate at 350 K350\text{ K}Rate at 400 K400\text{ K}
Compound W1.21.22.42.44.84.8
Compound X5.05.03.53.52.02.0
Compound Y0.80.80.80.80.80.8
Compound Z2.02.04.04.06.06.0

Based on the table, match each compound to its corresponding line or curve characteristic when translated into a rate versus temperature graph.

  • Compound WA concave-up curve illustrating a doubling rate for every 50 K50\text{ K} temperature increase
  • Compound XA straight line with a negative slope of −0.03 mmol/L⋅s⋅K−1-0.03\text{ mmol/L}\cdot\text{s}\cdot\text{K}^{-1}
  • Compound YA horizontal line with a slope of zero at a constant rate value of 0.8 mmol/L⋅s0.8\text{ mmol/L}\cdot\text{s}
  • Compound ZA straight line with a constant positive slope of 0.04 mmol/L⋅s⋅K−10.04\text{ mmol/L}\cdot\text{s}\cdot\text{K}^{-1}

Answer

Compound W matches the concave-up exponential curve; Compound X matches the negative slope of −0.03 mmol/L⋅s⋅K−1-0.03\text{ mmol/L}\cdot\text{s}\cdot\text{K}^{-1}; Compound Y matches the horizontal zero-slope line at 0.8 mmol/L⋅s0.8\text{ mmol/L}\cdot\text{s}; Compound Z matches the positive slope of 0.04 mmol/L⋅s⋅K−10.04\text{ mmol/L}\cdot\text{s}\cdot\text{K}^{-1}.
Each tabular dataset directly translates to a specific graphical shape or slope: exponential doubling yields a concave-up curve; equal decreases yield a linear negative slope of −0.03-0.03; constant values yield a zero-slope horizontal line; equal increases yield a linear positive slope of 0.040.04.

Step-by-Step Solution

1
Analyze Compound W's data trend
The rates are 1.21.2, 2.42.4, and 4.84.8 at 300 K300\text{ K}, 350 K350\text{ K}, and 400 K400\text{ K}.
Dividing consecutive rates yields 2.41.2=2\frac{2.4}{1.2} = 2 and 4.82.4=2\frac{4.8}{2.4} = 2, showing exponential growth (concave-up curve with a doubling pattern).
2
Analyze Compound X's data trend and calculate slope
Rate decreases from 5.05.0 to 3.53.5 to 2.02.0 as temperature rises from 300 K300\text{ K} to 400 K400\text{ K}.
The rate change per kelvin is 2.0−5.0400−300=−3.0100=−0.03 mmol/L⋅s⋅K−1\frac{2.0 - 5.0}{400 - 300} = \frac{-3.0}{100} = -0.03\text{ mmol/L}\cdot\text{s}\cdot\text{K}^{-1}.
3
Analyze Compound Y's data trend
The rate remains unchanged at 0.8 mmol/L⋅s0.8\text{ mmol/L}\cdot\text{s} across all temperatures.
A constant value across the independent variable axis translates to a horizontal line with zero slope.
4
Analyze Compound Z's data trend and calculate slope
Rate increases linearly from 2.02.0 to 4.04.0 to 6.06.0.
The slope is 6.0−2.0400−300=4.0100=0.04 mmol/L⋅s⋅K−1\frac{6.0 - 2.0}{400 - 300} = \frac{4.0}{100} = 0.04\text{ mmol/L}\cdot\text{s}\cdot\text{K}^{-1}.

Key Concept

Translating Data Formats between Tables and Linear/Non-linear Graphical Features
Rate this question

Topics

Translating Data Formats

More questions from this topic