chemistry lab molar volume of a gas copy
TRANSCRIPT
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Molar Volume of a Gas
General Chemistry Laboratory CHEM-A107-025
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Abstract
Magnesium ribbon is being reacted with hydrochloric acid to obtain a molar
volume of hydrogen gas that is given off. This reaction takes place in a gas collection
apparatus to efficiently obtain accurate results. Applying several corrections the standard
molar volume is determined with a slight percent deviation. These errors are due to
discrepancies in the reaction itself. Hydrogen gas may have partially dissolved into the
water and/or not fully reacted with the magnesium.
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Introduction
Molar volume is the volume filled by a single mole of a certain gas. One mole of
any gas contains 6.022 x1023 molecules. According to the ideal gas law, ideally behaving
gases will abide by the following:
P x V = N x R x T (1)
where P is the pressure of the gas (atm), V is the volume of the gas (L), N is the number
of molecules in the gas (mole), R is the gas constant (L atm / mole K), and T is the
temperature of the gas (K). This equation can be employed as a solution to determine the
molecular mass of a gas.
The questions at hand are: What is the molar mass of H2 (g)? How does one find
this? The purpose of this experiment is to determine the molar mass of H2 (g) (which can
be assumed to behave as an ideal gas). To achieve this, one must determine the volume of
hydrogen gas produced from the reaction of certain amounts of magnesium and
hydrochloric acid. The chemical equation is as follows:
Mg(s) + 2HCl(aq) MgCl2(aq) + H2(g) (2)
The acid (HCl), which provides hydrogen ions, reacts with magnesium to generate
hydrogen gas as demonstrated in the previous equation. This reaction is called an
Oxidation Reduction reaction because the ions are exchanged as well as the electrons in
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the reagents. In this particular reaction oxidation occurs when one reagent looses
electrons and the other is reduced.
How can this be applied to the real world? Many of the materials one handles in
the chemistry lab are gases. Most of the time it is a simple process to measure the
volume of a sample of gas rather than to measure its mass.
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Experimental
First a piece of magnesium ribbon was buffed with a piece of Emory cloth in
order to remove any oxide coating and immediately following was dusted. Using a
Mettler analytical balance, the magnesium ribbon was weighed and its mass recorded
(0.0264g). The magnesium ribbon was then coiled and attached to a short copper wire.
A gas collection apparatus was constructed using a beaker, gas collection tube,
and rubber stopper (Figure A). A beaker was filled about ¾ of the way full with water.
The tube was filled with 5.0 mL of 12 M hydrochloric acid and topped off with deionized
water. The copper wire was inserted into the rubber stopper and fastened securely to the
test tube. The test tube was then inverted and placed into the water being careful not to
allow any air to enter. The hydrochloric acid slowly distributed to the magnesium coil,
reacting thus producing bubbles of hydrogen gas. Five minutes later, allowing the
temperature to regulate and the remaining bubbles to rise, the test tube was attended to.
The water in the tube and the water in the beaker were then brought to the same level by
adjusting the height of the water in the test tube with the water in the beaker. The amount
of hydrogen gas captured in the test tube is observed and recorded (27.3 mL). The
temperature and pressure of the laboratory were then recorded as 294.9 K and 762 mm
Hg respectively.
This regimen is repeated once more with minor adjustments. The equipment was
thoroughly cleansed before beginning the second trial. The amount of magnesium ribbon
was slightly increased (0.028 g). Upon observing the new reaction, the amount of
hydrogen captured in the test tube was again recorded (27.6 mL). The temperature and
pressure in the laboratory remained constant.
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Results and Discussion
The function of this lab is to establish the molar volume of a sample of hydrogen
gas utilizing the Gas Collection Apparatus, examine the mass-volume relationships in a
chemical reaction, and familiarize the relationship between density and molecular mass
of a gas. The temperature and pressure of the laboratory were recorded as 294.9 K and
762 mm Hg respectively. The observed molar volumes of the hydrogen gas were
measured to be 27.3 mL and 27.6 mL respectively. Because the water levels in the test
tube and the beaker were unable to be equaled manually, the following equation was used
to correct the pressure for difference in water levels.
Ptot = barometric pressure + (∆L x 0.0753 torr / cm) (3)
Where Ptot is total pressure (cm Hg) and ∆L is the difference in the levels of the
water in the test tube and beaker. The adjusted pressures were calculated to be 746.19
mm Hg and 746.56 mm Hg respectively. After the first correction to pressure, a second
correction took place because the gas contains a significant amount of water vapor.
Dalton’s law of partial pressures states that the total pressure of a mixture of gasses is
equal to the sum of partial pressures of the individual components. Thus, this law is
applied to give the partial pressure of the hydrogen gas. The partial pressure of water in
the mixture was found from the following table. These values were then used in the
following equation.
PH2 = Ptot – PH2O
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(4)
Temperature (K) Pressure (mm Hg) Temperature (K) Pressure (mm Hg)
288 12.8 296 21.1
289 13.6 297 22.4
290 14.5 298 23.8
291 15.5 299 25.2
292 16.5 300 26.7
293 17.5 301 28.3
294 18.7 302 30.0
295 19.8 303 31.8
(Table A)
The partial pressures were calculated and recorded as 726.39 mm Hg and 726.76
mm Hg respectively. Next, the measured volume was adjusted to standard pressure and
temperature using the ideal gas law to determine the volume of the hydrogen gas.
PH2 x Vobs Pstd x Vstp
Tobs Tstd (5)
Where P is pressure (mm Hg), V is volume (mL), and T is temperature (K). The
adjusted volumes were calculated and recorded as 24.15 mL and 24.43 mL respectively.
To find the experimental standard molar volumes of hydrogen gas, the previously
calculated data is divided by the number of moles of magnesium ribbon used in each trial
(0.0011 and 0.0012 moles respectively).
=
8
X__ moles Mg
(6)
Where X is the adjusted volumes according to equation five. The experimental
standard molar volumes of hydrogen gas were calculated and recorded as 21.955 L and
20.361 L respectively. To determine the density of hydrogen gas at STP, the experimental
results are used in the following equation.
MM__Vmol
(7)
Where D is density, MM is the molar mass of hydrogen gas, and V is the
experimental standard molar volume of hydrogen gas. The density of hydrogen gas is
determined to be 0.092 g/mL and 0.099 g/mL respectively.
The major source of error for this particular experiment is in the reaction. The
magnesium ribbon may have only partially reacted and the hydrogen gas may have
dissolved in the water. Both of these scenarios yield skewed results, with a lower molar
volume being observed. The original observed volume of the gas would have been lower
effecting all calculations proceeding. Another possible source of error is the equipment
and whether it was used and/or working properly. The percent deviation for the results
can be calculated by the following equation. The theoretical molar volume of an ideal gas
is 22.4 L. The percent deviation was calculated for the two trials and resulted in 1.99%
and 9.10% respectively.
Experimental standard molar volume
=
D =
9
(Theoretical – Experimental)Theoretical
(8)
Conclusions
The purpose of this experiment was to find the molar volume of hydrogen gas by
reacting magnesium and hydrochloric acid. Observations and calculations concluded a
closely accurate result of the molar volume of hydrogen gas. Data also proves that in this
experiment magnesium was the limiting reagent and the hydrochloric acid the excess
reagent.
References
(1) Loyola University Department of Chemistry, General Chemistry Laboratory
ChemA107; New Orleans, LA, 2006; pp 39-42.
(2) Wikipedia contributors, Wikipedia, The Free Encyclopedia; 2006,
http://en.wikipedia.org/wiki/Main_Page.
Actual Val ue- Experimental Value Actual Val ue
X 100 [ ] % Error = Abs
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Calculations
Sample calculations of pressure, volume, density, and percent deviation:
P x V = N x R x T
Mg(s) + 2HCl(aq) MgCl2(aq) + H2(g)
Ptot = barometric pressure + (∆L x 0.0753 torr / cm) = 76.2 mm Hg – (21.5 x 0.07353 mm Hg/cm) = 746.19 mm Hg
PH2 = Ptot – PH2O = 746.19 – 19.8 = 726.39 mm Hg
PH2 x Vobs Pstd x Vstp(726.39)(27.3) (760)(Vstp)
Tobs Tstd 294.9 273
Vstp = 24.5 mL
X__ 24.15 mL = 21.955 L moles Mg 0.0011 moles
MM_ 2.016 0.092 g/mL Vmol 21.955
22.4 – 21.955 22.4
=
Experimental standard molar volume
=
D =
Actual Val ue- Experimental Value Actual Val ue
X 100 [ ] % Error = Abs
=
=
=
=
=
=
x 100 = 1.99%