Gas stoichiometry

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Objectives

Explore an acid / base reaction that produce \(\ce{CO2}\)
Determine the molar mass of \(\ce{CO2}\) using the ideal gas law
Use stoichiometry to calculate actual and theoretical yield of product
Evaluate and make suggestions to improve the experiment each trial
Quantify the accuracy of your measurements

Safety and Notes

Handle the hydrochloric acid, HCl, carefully. It is a strong acid and can cause burns to skin and eyes.
Make sure you use the designated test tubes and wash bottles for this experiment, or you may get a test tube stuck in the bottle.

Introduction

Chemical reactions involving acids and bases are an important and ubiquitous type of chemical reaction. In this laboratory experiment, we’ll investigate acid base reactions involving carbonates that generate carbon dioxide gas, \(\ce{CO2}\). You may have seen this type of reaction in action in one of the favorite projects of science fairs: the baking soda volcano. To cause the “eruption”, baking soda (sodium bicarbonate, which acts as the base) is mixed with vinegar (acetic acid) which causes bubbles of carbon dioxide to form and causes a foamy eruption. Check out this video for instructions to make a volcano. Acid base reactions are also important in the environment. One example acid base reaction involving carbonates can be seen by the deterioration of limestone statues and buildings (which contain calcium carbonate) exposed to acid rain over time. Washington D.C. has many examples of buildings and monuments that are damaged by acid rain, which is highlighted in this video.

In this lab, you’ll quantitatively determine the amount of carbon dioxide gas formed from this acid base reaction and use that to calculate an experimental molar mass of carbon dioxide. To “capture” the gas generated, you’ll conduct the reaction in a closed wash bottle, and the gas generated will displace the water in the wash bottle. The experimental set-up is shown in the image below. The amount of water that is displaced will give the volume of the gas generated, V_\(\ce{CO2}\).

There are three quantities we will use to describe how much carbon dioxide was generated: mass, volume and chemical amount. We can measure the mass m on a balance, in units of grams (g) or milligrams (mg). We can determine the volume of the gas V_\(\ce{CO2}\) by measuring the volume of displaced water. We don't have a direct way to measure the chemical amount n; here, we use the ideal gas law to figure out the chemical amount of carbon dioxide from its volume. The chemical amount uses units of moles (mol); when two samples have the same chemical amount, they contain the same number of particles. If you determine both the chemical amount and the mass in a specific sample, as you will in this experiment (i.e. how much you have in moles as well as grams), you can use those values to calculate the molar mass of a substance (units are grams per mole, g mol^_-1). The molar mass of a substance is a value unique to the specific element or compound.

The acid base neutralization reaction we’ll investigate is hydrochloric acid (\(\ce{HCl}\)) with sodium bicarbonate (\(\ce{NaHCO3}\)). \(\ce{HCl}\) is a monoprotic, strong acid. Monoprotic means it has one proton (\(\ce{H+}\)), and a strong acid means it completely dissociates so all the \(\ce{HCl}\) molecules completely break apart into \(\ce{H+}\) and \(\ce{Cl-}\) ions. The right pointing arrow in Reaction 1 indicates the complete dissociation of the \(\ce{HCl}\), which breaks down completely into \(\ce{H+}\) and \(\ce{Cl-}\) ions. Reaction 2 shows the balanced acid base neutralization reaction. Notice how each reactant and product is in a 1:1 mole for this particular reaction. This means that if you have 5 moles of \(\ce{NaHCO3}\), you will form 5 moles of \(\ce{CO2}\) gas, provided there is an excess of \(\ce{HCl}\). The molar ratios given in your balanced equation are always important in stoichiometry calculations.

\[\ce{HCl(aq) -> H+(aq) + Cl-(aq)}\tag{Reaction1}\]

\[\ce{ HCl(aq) + NaHCO3(aq) -> H2O(l) + NaCl(aq) + CO2(g)}\tag{Reaction2}\]

While collecting and analyzing your experimental data, you can focus on achieving good accuracy and precision. Recall that good accuracy means that your measurements are close to the “true” or “theoretical” value. Good precision means that you have multiple measurements that are close to each other. We can perform different calculations to quantify the accuracy and precision of measurements. To determine accuracy, the percent error is a simple calculation that is commonly used, shown in Equation 1. The “actual” value is the amount you calculate based on your experimental measurements. The “theoretical” value is the “true” value, which in this case is a known value that you can look up in a reputable reference.

Equation 1 – percent error

\[\frac{\mathrm{actual} - \mathrm{theoretical}}{\mathrm{actual}} * 100 \]

To express the precision, you must have more than one measurement so you can compare how close they are to each other. You can calculate a standard deviation and then relative standard deviation to express your precision as a percent, shown in Equations 3 and 4. You can do these calculations by hand, or you could use Excel or Google Sheets and utilize the built-in calculations for these statistics.

Equation 2 – average, \( \overline{x} \)

\( \overline{x} = \frac{1}{n} \sum_{i=1}^{n} x_{i} \)

Equation 3 – standard deviation, s

s =\( \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \overline{x})^2} \)

Equation 4 – relative standard deviation, RSD

RSD = \( \frac{s}{\overline{x}} * 100 \)%

You want to work carefully to obtain good accuracy and precision, but chemical reactions in practice are a bit more complicated than how they look on paper, so there are always physical limitations beyond your control that limit how much product can form. There are also limitations in the equipment you use that contribute to uncertainty in your measurements. In addition, poor experimental techniques or mistakes will also decrease the accuracy and precision you obtain. In this lab, you’ll conduct the experiment multiple times and improve your procedure and techniques each trial.

Experimental Procedure

Record observations and calculations in your lab notebook and on this summary sheet you will hand in at the end of class.

Task 1: Experimentally Determine the Molar Mass of Carbon Dioxide

Look up the molar mass of carbon dioxide and record this value as the “known” molar mass value (g/mol). In this procedure, you’ll follow a method to measure the values needed to experimentally determine the molar mass value.
First prepare your wash bottle, which will act as your experimental set-up. You may refer to the picture in the introduction as an example. Fill the wash bottle with tap water up to the fill line on the bottle. To get the water level to the fill line, it might be easier to overfill the bottle and then squirt out the excess. Place the wash bottle on the stir plate. Place a 150 or 250 mL beaker below the spout of the wash bottle and adjust to catch the displaced liquid.
Next prepare your test tube that will contain the acid base chemical reaction that will generate \(\ce{CO2}\). Weigh an empty gelatin capsule and record the mass. Fill the capsule with less than 0.50 g of sodium bicarbonate and weigh and record the exact mass of the full capsule. You can find the mass of just the sodium bicarbonate by the difference of the full and empty capsule to make sure you are under 0.50 g.
Into a 6-inch test tube, put in a small stir bar and add 7-10 mL 4 M HCl. Weigh the full test tube and record its mass. To weigh the test tube, you may want to tare a beaker on the scale and then put the test tube in the beaker to get its mass. Then place the test tube upright into the wash bottle.
To start the reaction, drop the filled gelatin capsule into the test tube containing the acid. Working quickly but carefully, use a glass stir rod to poke the capsule to ensure it is not stuck on the test tube wall and that it is sitting in the acid. Close the lid of the wash bottle tightly. It will take a minute or so, but the acid will dissolve the gelatin capsule and you’ll see the reaction between the acid and the bicarbonate. The carbon dioxide generated will displace the water in the wash bottle. The water will be displaced quickly at first, so be careful to capture all the water that is displaced from the reaction. Once the reaction appears complete (the water stops dripping from the wash bottle), slowly turn on the stirring. You want to ensure that the capsule or sodium bicarbonate did not get stuck to the inside of the test tube. Stir for about 5 minutes or until the reaction is complete, the capsule and sodium bicarbonate are totally dissolved, and no more water is displaced.
Move the beaker containing the displaced water away from the wash bottle. Open the lid of the wash bottle just enough to insert a thermometer into the top of the wash bottle where the generated carbon dioxide is and record the temperature (T_\(\ce{CO2}\)).
Carefully remove the test tube from the wash bottle. Dry off the water from the outside of the test tube. Weigh the test tube which now contains any leftover reactants and the aqueous products and record the mass. From the initial mass and this final mass, calculate the mass of \(\ce{CO2}\) formed.
Measure the volume of the displaced water in the beaker by pouring it carefully into a large graduated cylinder. Pay attention to the markings on the graduated cylinder. If the total volume of water is more than the max volume in the graduated cylinder, you’ll have to measure it in increments and sum up the measurements. The volume of the displaced water is the same as the volume of the carbon dioxide that was formed (V_\(\ce{CO2}\)).
Record the atmospheric pressure in the laboratory. Since the apparatus you set up is open to the atmosphere, the atmospheric pressure is the same as the pressure of the carbon dioxide (P_\(\ce{CO2}\)).
Complete all your observations and calculations for Trial 1 before moving on.
Repeat this entire procedure in Trial 2 to get a second calculated value for molar mass of \(\ce{CO2}\).
Clean up by cleaning and returning your stir bar. Be careful not to drop the stir bar in the sink. Dispose of all hazardous waste in the labeled container in the hood. Clean all other glassware and equipment used and return it or put it away. Wipe off and dry the counter. Wash your hands before leaving the lab.

Acknowledgement

Parts of this lab were adopted from Nayasulu, F., Paris, S., and Barlag, R. Wash Bottle Laboratory Exercises: Mass of \(\ce{NaHCO3}\) in an Alka-Seltzer Tablet, Molar Mass of \(\ce{CO2}\), and the Ideal Gas Law Constant. J Chem Ed. 2009, 86, 842-844.