Problem 56 - Chemistry and Chemical Reactivity

Question

A The density of pure water is given at various temperatures. $$\begin{array}{ll} \hline T\left(^{\circ} \mathrm{C}\right) & d\left(\mathrm{g} / \mathrm{cm}^{3}\right) \\ \hline 4 & 0.99997 \\ 15 & 0.99913 \\ 25 & 0.99707 \\ 35 & 0.99406 \\ \hline \end{array}$$ Suppose your laboratory partner tells you that the density of water at \(20^{\circ} \mathrm{C}\) is \(0.99910 \mathrm{g} / \mathrm{cm}^{3} .\) Is this a reasonable number? Why or why not?

Step-by-Step Solution

Answer

The density should be lower than 0.99913 g/cm³. The partner's value is unreasonable.

Step 1: Understand the Density Values

The table provides the densities of water at specific temperatures. Notice that as the temperature increases from 4°C to 35°C, the density of water decreases from 0.99997 g/cm³ to 0.99406 g/cm³. This trend implies that water has a lower density at higher temperatures.

Step 2: Identify Known Values

We are given the following densities:\(T(15^{\circ}\mathrm{C}) = 0.99913 \mathrm{g}/\mathrm{cm}^3\)\(T(25^{\circ}\mathrm{C}) = 0.99707 \mathrm{g}/\mathrm{cm}^3\)

Step 3: Analyze the Midpoint Temperature

The temperature of 20°C lies between 15°C and 25°C. The density should logically lie between the densities at these two temperatures, namely between 0.99913 g/cm³ and 0.99707 g/cm³, following the decreasing trend.

Step 4: Evaluate Partner's Claim

Your partner's claim is that at 20°C, the density is 0.99910 g/cm³. Compare this to the calculated range: - Your partner's density is nearly equal to the density at 15°C (0.99913 g/cm³), but substantially higher than the midpoint density (about 0.99810 g/cm³) expected given the trend. - Therefore, the partner's reported density is higher than expected for 20°C based on the observed trend of decreasing density with increasing temperature.

Step 5: Conclusion

Since 0.99910 g/cm³ is not between 0.99913 g/cm³ and 0.99707 g/cm³, the density reported by your partner is unlikely to be correct.

Key Concepts

Temperature Effect on Density

Water exhibits unique properties when it comes to density variations with temperature. As the temperature rises, molecular activity within the water increases, causing the molecules to move further apart. This increase in molecular spacing results in a decrease in density.
In the specific case of water, it is denser at 4°C compared to higher temperatures. At 4°C, water reaches its maximum density point, around 0.99997 g/cm³, which is an important anomaly of water compared to most other substances. As temperatures increase from this point, the density decreases.
This phenomenon can be observed in everyday life. For instance, ice, being less dense, floats on liquid water, and warmer upper layers of water bodies show different density gradients compared to cooler lower layers. Understanding how temperature affects the density of water is crucial for various applications, from climatology to engineering, as it affects buoyancy, aquatic environments, and energy efficiency.

Density Trends

The trend in water density with temperature increase is notably consistent. From a temperature of 4°C to around 35°C, the density of water steadily decreases.
In the given dataset:

• At 4°C, the density is 0.99997 g/cm³.
• At 15°C, the density decreases to 0.99913 g/cm³.
• By 25°C, it further reduces to 0.99707 g/cm³.
• At 35°C, the density drops again to 0.99406 g/cm³.

These measurements clearly illustrate that as temperature increases, the density of water decreases. This downward trend is due to enhanced molecular agitation at higher temperatures, which encourages expansion and less compactness in the water structure.
It is important to understand this trend as it helps predict how water will behave under changing thermal conditions, which is useful for scientific experiments and industrial processes.

Density Values Analysis

When examining density data, it's crucial to evaluate whether given or new reported values align with known trends. In the exercise scenario, the partner suggests a water density of 0.99910 g/cm³ at 20°C.
First, notice that 20°C is between the tabulated 15°C and 25°C. Given the trend, one can conclude that the density should logically fall between 0.99913 g/cm³ for 15°C and 0.99707 g/cm³ for 25°C.
For broader insight, if you do a quick calculation, a midpoint rough estimate between 15°C and 25°C densities would suggest that around 0.99810 g/cm³ would be more reasonable for 20°C. However, the given partner's value of 0.99910 g/cm³ is closer to the earlier 15°C figure, signaling an inconsistency with expected trends.
This analytical approach of comparing values is essential for accuracy in studies and during peer review processes, ensuring that data not only supports hypotheses but also adheres to known scientific principles.