# Experiment_620_Calculation of the Ideal Gas Constant_1_1_3

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

 Student Name Laboratory Date:  Date Report Submitted: ___________________________ Student ID Experiment Number and Title Experiment 620:  Calculation of the Ideal Gas Constant

Experiment 620:  Calculation of the Ideal Gas Constant

Section 1:  Purpose and Summary

Determine the value of the ideal gas constant, R, by measuring the volume, temperature, and pressure of a known amount of gas.

Under ordinary conditions, the pressure (P) of any sample of an ideal gas is inversely proportional to its volume (V) and directly proportional to its absolute temperature (T) and to the number of moles (n) of the gas present in the sample. This proportionality may be written:

$$\mathrm{P} \alpha \frac{\mathrm{nT}}{\mathrm{V}}$$

where α is read "is proportional to." It is more convenient to put this relationship in the form of an equation:

$$P=\frac{n R T}{V}$$

where R, the “proportionality constant” is usually called the “ideal gas constant.” This equation is more familiar in the rearranged form PV = nRT, and this equation is called the “ideal gas equation” or the “ideal gas law.”

The purpose of this experiment is to verify this equation for a sample of hydrogen gas, H2 (g). To do this, we must measure P, V, T, and n. The value of R can then be calculated and compared with the accepted value of R. In this experiment, P, V, and T will be measured directly, while n will be calculated from the amount of magnesium used to produce the hydrogen gas from reacting with hydrochloric acid according to the equation:

Mg(s) +  2 HCl (aq)    → MgCl2 (aq)   + H2 (g

Section 2:  Safety Precautions and Waste Disposal

Safety Precautions:

Use caution when handling 6 M HCl. It is corrosive and can burn your skin. If any HCl comes into contact with your skin, rinse it off immediately and thoroughly with lots of water.

Confirm that access to an eyewash station is available and know where it is.  6 M HCl is an eye hazard.

Waste Disposal:

At the end of the experiment, the HCl solution will be much more dilute. The water, diluted HCl and MgCl2 mixture may be rinsed down the sink with plenty of water.

Section 3: Procedure

Section 4 Calculations

For each sample of H2 gas you collected in Part 1, you collected enough data to determine its pressure, volume, number of moles, and temperature.  When you substitute your values of P, V, n, and T into the ideal gas law, PV = nRT, you will be able to determine your own value of R, the ideal gas constant.

 Trial 1 Trial 2 Number of Moles (n): From the mass of magnesium used and the balanced equation, calculate the number of moles of hydrogen gas expected for each trial.    Show your equation here: (f)  n = _________ mol H2 (f)  n = _________ mol H2 2. Pressure (P):  To calculate the partial pressure of hydrogen in the tube, there are two corrections to take into account.  The first correction has to do with the fact that the hydrogen gas was collected over water.  The gas in the eudiometer is really a mixture of hydrogen gas and water vapor.  The contribution of water to the total pressure is called the vapor pressure of water.  It depends on temperature and can be looked up in a chemistry handbook.  To find the vapor pressure of water in your experiment, look up “water, vapor pressure” in the CRC Handbook of Chemistry and Physics.  There will be a table that shows the vapor pressure of water (in mmHg) for any given temperature (in °C).    The second correction has to do with the difference in water levels in the eudiometer and in the beaker.  If the levels were equal, then the pressure inside and outside would be equal. When the levels are unequal, it means that the atmosphere and the gas inside the eudiometer are not pushing down equally on the surface of the water.  The difference in water levels that you measured corresponds to the pressure difference in units of mmH2O. This can be converted to mmHg, using the relation 13.6 mmH2O = 1 mmHg:     Pcorr = (c) x $$\frac{1 \mathrm{~mm} \mathrm{Hg}}{13.6 \mathrm{~mm} \mathrm{H}_{2} \mathrm{O}}$$     Taking both corrections into account:  P(H2) = (e) – (g) – (h)    Convert the pressure of H2 to atm. (g)  PH2O = _______ mmHg                    (h)  Pcorr = _______ mmHg                (i)  P(H2) = ________ atm (g)  PH2O = _______ mmHg                    (h)  Pcorr = _______ mmHg                (i)  P(H2) = ________ atm 3. Volume (V): For each trial, convert the volume of gas (b) from mL to L. (j)  V(H2) = ________ mL (j)  V(H2) = ________ mL 4. Temperature (T): For each trial, convert the temperature (d), from °C to K. (k)  T(H2) = ________ K (k)  T(H2) = ________ K 5. Using the Ideal Gas Law, PV = nRT, calculate an experimental value for R for each trial.  R = $$\frac{P V}{n T}=\frac{(i) \mathrm{x}(j)}{(f) \mathrm{x}(k)}$$ Rexptl = _____________ Rexptl = _____________ 6. Report the value of R obtained for each trial and the average value.   $$R_{\text {average }}=\frac{R_{\text {trial } 1}+R_{\text {trial } 2}}{2}$$ Raverage = _____________________________ 7. Calculate the percent error using the theoretical value of R (0.08206 L•atm/K•mol) and your average experimental value of R.  error $$\%=\frac{\left|R_{\text {theoretical }}-R_{\text {average }}\right|}{R_{\text {theoretical }}} \times 100$$ % error = _____________________________

Show ALL work here:

Post Lab Questions:

1. Why don’t you need to measure the exact volume of acid used?

2. In a similar experiment, a piece of aluminum was reacted with HCl. The hydrogen gas produced was collected in a eudiometer in the same way.

a) Write and balance the equation for this reaction. (Hint: what is the formula of aluminum chloride, the other product?)

b) If 39.5 mL of H2 are produced at 21°C when the atmospheric pressure is 762.8 mmHg, and if the height of the liquid column in the eudiometer is 11.2 cm, what mass of aluminum was used?

Experiment_620_Calculation of the Ideal Gas Constant_1_1_3 is shared under a CC BY license and was authored, remixed, and/or curated by LibreTexts.