Thermal Dependency - Online Tutor, Practice Problems & Exam Prep

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

Hey everyone. So in this set of videos, we're going to take a look at the idea of thermal dependency. First of all, we're going to say that calibration is the process of measuring the actual quantity of mass, volume, and other chemical measurements that relate to what we observe on an analytical scale. Remember, analytical chemistry itself is the chemistry of precision and accuracy. We want to be as accurate and precise as possible and make sure we minimize any outside factors.

A way of doing this is by calibrating our instruments. In general, when taking the measurement of a solution, you must take into account any type of thermal expansion that occurs with solutions and instrumentation. To do this, we use a correction for thermal expansion, where \( c' \) represents the concentration of our solution, \( d' \) represents the density of our solution, \( c \) represents our new concentration of our solution, and \( d \) represents our new density of our solution. If we take a look here at this chart, we have temperatures ranging from 10 degrees Celsius all the way to 30 degrees Celsius, and with it, we have the density of water. Now remember, we're accustomed to seeing density as being 1, but that's only true at a specific temperature, pressure, and ideal conditions.

Most of the time, density is a value that's less than 1 and here we're seeing the varying forms of density with water. Here, we have the volume of 1 gram of water. So at these different temperatures, for example, at 10 degrees Celsius, we have a density here and at that temperature, this is the volume that we have. What this number is telling me is that at 10 degrees Celsius, we deliver 1.0014 milliliters of water for every 1 gram of water. But again, remember, analytical chemistry is the chemistry of accuracy and precision.

So we have to correct the basic glassware. And what we do here is we're going to correct it to 20 degrees Celsius. So here this is where the glassware is calibrated at 20 degrees Celsius, and by doing that, we get a more accurate read on the volume involved. It now becomes 1.0015 milliliters. When we're looking at this table, we can also make some observations.

From looking at this, we can come up with some ideas. What we can see here is that as we go from 10 degrees Celsius to 30 degrees Celsius, we can see that the temperature is increasing. As the temperature increases, what effect does that have on our density? Well, if you're looking, you can see that our density as we go from 10 degrees Celsius to 30 degrees Celsius, it's decreasing. Now, why would that happen?

So think about it, density equals mass over volume. And you learned in general chemistry that temperature and volume are connected to one another. If we're increasing our temperature, this is going to cause our volume to increase. Our mass is staying constant, but our volume is increasing as the temperature goes up. What overall effect does this have on our density?

Well, the numerator is staying the same but the denominator is increasing. This causes the density to decrease. Okay. So that's the connection we need to see here. This is one of the consequences of thermal expansion.

It can affect our density by affecting our volume. So now that we've looked at this table and talked about the idea of thermal expansion and the accuracy and precision involved, click on to the next video and let's continue with our discussion of thermal expansion.

Thermal Expansion

Hey everyone. So here it says, Massachusetts limits the amount of lead in drinking water to 219 parts per billion. So for part a, we need to express the total molarity, and for part b, what will happen to the molarity of the solution as the temperature increases? Will it increase, decrease, or remain constant? Alright, so let's first look at part a.

So here we're going to do part a up here, and remember that 1 part per billion is equal to 1 microgram per liter. With this information, we can then convert 219 parts per billion to 219 micrograms of lead per liter. All we have to do now is convert that to molarity, which is just moles over liters. So I'm going to first get rid of micrograms. Remember that 1 micro is equal to 10 to the negative 6. Micrograms cancel out, now we have grams per liter. Finally, we can say that 1 mole of lead according to the periodic table weighs 207.2 grams.

Grams cancel out, and now what we have at the end is moles over liters, which is molarity. So, plug that into your calculator, and you'll get 1.06×10-6 molarity for lead. So that's part A. Now for part B, what will happen to the molarity as the temperature increases? Well, remember that molarity itself represents moles over liters, and remember that temperature is connected to volume.

If we're increasing the temperature, then that means we're going to increase our volume. So, let's think about it. Our volume is increasing, so liters on the bottom would increase. Our moles are staying constant because we're not adding more of our solute. So, the numerator stays the same, the denominator, the bottom part, is increasing.

What overall effect does that have on molarity? Well, that'll cause molarity to decrease. So that would mean we'd expect our molarity to decrease as our temperature increases. So, here those would be our final answers for parts both A and B.

Thermal Dependency Calculations

It is stated that a 0.02135 molar aqueous solution is prepared at 21 degrees Celsius where the density is given as 0.9979955 grams per milliliter. What is the new concentration if the same experiment is performed a month later when the temperature is now 26 degrees Celsius with this new density? Alright. So, we're talking about different temperatures and, as a result, our density changes. Our formula here that we are going to use is:

c ' ρ ' = c ρ

We have our initial concentration as 0.02135 molar associated with this density. Hence, 0.9979955 grams per milliliter equals, when we are asked to find what the new concentration is, c / 0.9967867 grams per milliliter . Here, we will cross multiply these two numbers together and then these two terms together.

At this point, it gives me: 0.9979955 grams per milliliter × c ' = 0.02128136045 × molarity

Divide both sides now by 0.9979955 grams per milliliter . This cancels out with this and leaves our units in molarity:

So, the new concentration for my solution will be 0.02132 molar . Now, this answer makes sense because we know that when the temperature was 21 degrees Celsius, our concentration was 0.02135 molar. From our previous video, we said that if our temperature increases, this will cause an increase in volume. And because molarity equals moles over volume, that means that my molarity should decrease. And that's what we are seeing here.

Our molarity has indeed decreased, and now it's a new number of 0.02132 molar. Now that we've seen this example, come back and see if you can solve the next example here. So again, attempt it on your own and come back to see if you get the same answer as I do.

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

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.