Thermal Dependency: Videos & Practice Problems

Calibration in analytical chemistry ensures precision and accuracy in measurements, accounting for thermal expansion effects on solutions and instrumentation. As temperature increases, the density of water decreases due to the relationship between mass and volume. For instance, at 10°C, 1 gram of water occupies 1.0014 mL, while at 20°C, it adjusts to 1.0015 mL. Understanding this thermal dependency is crucial for accurate chemical analysis, as it directly impacts density calculations and overall measurement reliability.

Thermal Expansion

In the study of thermal dependency, calibration plays a crucial role in analytical chemistry, which emphasizes precision and accuracy in measurements. Calibration involves adjusting instruments to ensure that the quantities of mass, volume, and other chemical measurements align with observed values. This process is essential for minimizing external factors that could affect results.

When measuring solutions, it is important to consider thermal expansion, which can alter both the density and concentration of a solution. The correction for thermal expansion can be expressed with the following relationships: c' = c \cdot \frac{d'}{d}, where c' is the corrected concentration, d' is the corrected density, c is the new concentration, and d is the new density.

For example, the density of water varies with temperature, as shown in a table ranging from 10 degrees Celsius to 30 degrees Celsius. At 10 degrees Celsius, the density of water is approximately 1.0014 milliliters per gram, while at 20 degrees Celsius, it adjusts to 1.0015 milliliters per gram. This variation highlights that the commonly accepted density of 1 g/mL is only accurate under specific conditions.

As temperature increases, the density of water decreases. This phenomenon can be explained by the relationship between density, mass, and volume, expressed as Density = \frac{Mass}{Volume}. When temperature rises, the volume of water expands while the mass remains constant, leading to a decrease in density. This understanding of thermal expansion is vital for achieving accurate measurements in analytical chemistry, as it directly impacts the results obtained from experiments.

In summary, recognizing the effects of thermal expansion on density and the importance of calibration ensures that measurements in analytical chemistry are both accurate and precise, allowing for reliable data interpretation.

Thermal Expansion

In Massachusetts, the regulation limits the amount of lead in drinking water to 219 parts per billion (ppb). To convert this measurement into molarity, we start by recognizing that 1 ppb is equivalent to 1 microgram of lead per 1 liter of water. Therefore, 219 ppb translates to 219 micrograms of lead per 1 liter.

To find the molarity, which is defined as moles of solute per liter of solution, we first convert micrograms to grams. Since 1 microgram equals \(10^{-6}\) grams, we have:

219 micrograms = \(219 \times 10^{-6}\) grams.

Next, we need to convert grams to moles using the molar mass of lead, which is 207.2 grams per mole. The conversion is as follows:

\[\text{Molarity} = \frac{\text{moles}}{\text{liters}} = \frac{219 \times 10^{-6} \text{ grams}}{207.2 \text{ grams/mole}} \approx 1.06 \times 10^{-6} \text{ M}\]

Thus, the molarity of lead in the solution is approximately \(1.06 \times 10^{-6}\) M.

Regarding the effect of temperature on molarity, it is important to understand that molarity is defined as the number of moles of solute divided by the volume of the solution in liters. As temperature increases, the volume of the solution typically expands due to thermal expansion. Since the number of moles of lead remains constant (no additional solute is added), an increase in volume results in a larger denominator in the molarity equation.

Consequently, as the volume increases while the number of moles stays the same, the overall molarity will decrease. Therefore, we can conclude that the molarity of the solution will decrease as the temperature increases.

Thermal Dependency Calculations

In this scenario, we are examining how temperature changes affect the concentration of a solution. Initially, a 0.02135 molar aqueous solution is prepared at 21 degrees Celsius, with a density of 0.9979955 grams per milliliter. When the temperature rises to 26 degrees Celsius, the density changes to 0.99627867 grams per milliliter, prompting us to calculate the new concentration.

To find the new concentration, we utilize the relationship between concentration and density, expressed as:

\[ \frac{C'}{D'} = \frac{C}{D} \]

Here, \(C'\) represents the new concentration, \(D'\) is the new density, \(C\) is the initial concentration, and \(D\) is the initial density. Plugging in the known values:

\[ \frac{C'}{0.99627867} = \frac{0.02135}{0.9979955} \]

Cross-multiplying gives us:

\[ 0.9979955 \times C' = 0.02135 \times 0.99627867 \]

Calculating the right side:

\[ 0.02135 \times 0.99627867 \approx 0.02128136 \text{ grams per milliliter} \]

Now, we can isolate \(C'\) by dividing both sides by the initial density:

\[ C' = \frac{0.02128136}{0.9979955} \approx 0.02132 \text{ molar} \]

This result indicates that the concentration has decreased from 0.02135 molar to 0.02132 molar due to the increase in temperature, which causes an increase in volume. Since molarity is defined as moles of solute per liter of solution, an increase in volume leads to a decrease in molarity, confirming our calculations are consistent with the expected behavior of solutions under varying temperatures.

The mass of an empty container at 28 ^oC is 83.93 g. The mass of the container when filled with water from a 25-mL pipet is 108.70 g. Calculate the true volume of delivered water by the calibrated pipet.

• A. 24.8889 mL
• B. 24.8864 mL
• C. 24.8839 mL
• D. 24.8815 mL

Answer: (B)

Here’s what students ask on this topic:

What is thermal dependency in analytical chemistry?

Thermal dependency in analytical chemistry refers to the influence of temperature on the physical properties of substances, such as density and volume. As temperature changes, these properties can vary, affecting the accuracy and precision of measurements. For instance, the density of water decreases as temperature increases, which can impact the calibration of instruments and the reliability of chemical analyses. Understanding thermal dependency is crucial for making accurate corrections and ensuring precise measurements in analytical procedures.

How does temperature affect the density of water in analytical chemistry?

In analytical chemistry, temperature has a significant effect on the density of water. As temperature increases, the volume of water expands while its mass remains constant. This results in a decrease in density, as density is defined by the equation:

$\rho =\frac{m}{V}$

where $\rho$ is density, $m$ is mass, and $V$ is volume. For example, at 10°C, 1 gram of water occupies 1.0014 mL, but at 20°C, it occupies 1.0015 mL. This decrease in density with increasing temperature must be accounted for in precise measurements.

Why is calibration important in analytical chemistry?

Calibration is crucial in analytical chemistry because it ensures the accuracy and precision of measurements. By calibrating instruments, we can correct for any deviations caused by factors such as thermal expansion. This process involves adjusting the instruments to known standards, which helps in obtaining reliable and reproducible results. For example, calibrating glassware at 20°C accounts for thermal expansion, providing more accurate volume measurements. Without proper calibration, measurements could be inaccurate, leading to erroneous conclusions in chemical analyses.

What is the relationship between temperature and volume in the context of thermal expansion?

The relationship between temperature and volume in the context of thermal expansion is direct; as temperature increases, the volume of a substance also increases. This is because the molecules move more vigorously at higher temperatures, causing them to occupy more space. In analytical chemistry, this relationship is crucial for understanding how temperature changes can affect the volume of solutions and, consequently, their density. For instance, as the temperature of water increases from 10°C to 30°C, its volume increases, leading to a decrease in density.

How do you correct for thermal expansion in analytical measurements?

To correct for thermal expansion in analytical measurements, you need to adjust the observed values to a standard temperature, typically 20°C. This involves using correction factors that account for the changes in volume and density due to temperature variations. For example, if you measure the volume of water at 10°C, you would use a correction factor to adjust this volume to what it would be at 20°C. This ensures that your measurements are accurate and consistent, regardless of the temperature at which they were taken.