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Chapter 5: Problem 58

You have purchased a gas cylinder that is supposed to contain 5.0 mole \(\% \mathrm{Cl}_{2}(\pm 0.1 \%)\) and \(95 \%\) air. The experiments you have been running are not giving reasonable results, and you suspect that the chlorine concentration in the gas cylinder is incorrect. To check this hypothesis, you bubble gas from the suspicious cylinder through \(2.0 \mathrm{L}\) of an aqueous NaOH solution (12.0 wt\% NaOH, SG = 1.13) for exactly one hour. The inlet gas is metered at a gauge pressure of \(510 \mathrm{mm} \mathrm{H}_{2} \mathrm{O}\) and a temperature of \(23^{\circ} \mathrm{C}\). Prior to entering the vessel, the gas passes through a flowmeter that indicates a flow rate of \(2.00 \mathrm{L} / \mathrm{min}\). At the conclusion of the experiment, a sample of the residual \(\mathrm{NaOH}\) solution is analyzed and the results show that the \(\mathrm{NaOH}\) content has been reduced by \(23 \% .\) What is the concentration of \(\mathrm{Cl}_{2}\) in the cylinder gas? (Assume the \(\mathrm{Cl}_{2}\) is completely consumed in the reaction \(\mathrm{Cl}_{2}+2 \mathrm{NaOH} \rightarrow \mathrm{NaCl}+\mathrm{NaOCl}+\mathrm{H}_{2} \mathrm{O}\)

Short Answer

Expert verified
The concentration of \(\mathrm{Cl}_{2}\) in the cylinder gas can be calculated by comparing the experimental and theoretical Cl鈧� consumptions.

Step by step solution

01

Determine the consumption of NaOH

From the analysis, it is known that the NaOH content is reduced by 23 percent. The initial amount of NaOH is calculated by multiplying its volume (\(2.0L\)), its specific gravity (\(1.13g/mL\)), and its weight percentage (\(0.12\)). The sodium hydroxide consumed is therefore \(0.23\) of the initial amount.
02

Determine the amount of Cl鈧� from the stoichiometric reaction

According to the stoichiometry of the reaction (\(\mathrm{Cl}_{2}+2\mathrm{NaOH} \rightarrow \mathrm{NaCl}+\mathrm{NaOCl}+\mathrm{H}_{2}\mathrm{O}\)), 1 mole of Cl鈧� reacts with 2 moles of NaOH i.e. the amount required is \( \frac{1}{2} \) the moles of NaOH consumed.
03

Determine the amount of Cl鈧� from the flowmeter reading

The amount of Cl鈧� that should have passed through the system, assuming it is 5.0 mole \% Cl鈧�, can be found by calculating the molar flow rate of Cl鈧� (from the flowmeter reading of \(2.00 L/min\) and the gas law at the given pressure and temperature) and the duration of the experiment (1 hour). The mol percent is then used to determine the actual mole flow rate of Cl鈧�.
04

Compare the theoretical and experimental measurements

If the 5.0 mole \% Cl鈧� is accurate, the molar quantity from Step 2 should match the molar quantity from Step 3. The actual chlorine content is therefore calculated by using the ratio of the measured consumption (Step 2) to the theoretical consumption (Step 3).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Stoichiometry
Stoichiometry is a fundamental concept in chemistry that involves using relationships between reactants and products in a chemical reaction to determine quantitative data. In this exercise, we explore the reaction of chlorine gas (\(\mathrm{Cl}_{2}\)) with sodium hydroxide (\(\mathrm{NaOH}\)) to understand the amount of \(\mathrm{Cl}_{2}\) present in a gas mixture.

When analyzing stoichiometry, the coefficients of a balanced chemical equation tell us the ratio between reactants and products. In the given reaction, \(\mathrm{Cl}_{2}+2\mathrm{NaOH} \rightarrow \mathrm{NaCl}+\mathrm{NaOCl}+\mathrm{H}_{2}\mathrm{O}\), one mole of chlorine reacts with two moles of sodium hydroxide. This 1:2 ratio allows us to calculate how much \(\mathrm{Cl}_{2}\) corresponds to the \(\mathrm{NaOH}\) consumed.
  • To find \(\mathrm{Cl}_{2}\) usage, find the amount of \(\mathrm{NaOH}\) used, then half it (since 2 moles of \(\mathrm{NaOH}\) react with 1 mole of \(\mathrm{Cl}_{2}\)).
  • This calculation is grounded in the precise ratios given by stoichiometry.
Gas Laws
Gas laws provide necessary insights into the behavior of gases under various conditions, which helps us determine the concentration of chlorine in the gas cylinder during the experiment. The main gas law used in this scenario is the Ideal Gas Law, expressed as \(PV = nRT\).

The Ideal Gas Law relates pressure (\(P\)), volume (\(V\)), mole number (\(n\)), the gas constant (\(R\)), and temperature (\(T\)). This relation is vital to calculate the molar flow rate of \(\mathrm{Cl}_{2}\) in the gas cylinder.
  • Start by converting measured conditions like pressure and temperature to standard units.
  • Use flow meter data to compute how many moles of gas flow through the system per minute.
  • Adjust the flow quantity over an hourly duration to estimate the total \(\mathrm{Cl}_{2}\) transferred.

Practical Considerations

Remember, real gases may deviate slightly from ideal behavior due to interactions between gas molecules. However, the Ideal Gas Law provides a good approximation for this purpose when conditions are not extreme.
Experimental Error Analysis
In experimental chemistry, acknowledging and analyzing potential errors is crucial for solidifying your experimental conclusions. By understanding and accounting for these errors, you can accurately interpret your findings.

In this scenario, variances between the expected and experimental results suggest potential experimental errors. Some reasons for these errors could be:
  • Inaccurate flow meter readings which can alter the perceived gas flow rate.
  • Environmental conditions鈥攍ike temperature fluctuations鈥攏ot accounted for during calculations.
  • Incomplete chemical reactions, meaning not all gas reacted as expected, possibly due to impurities or inefficiencies in the setup.
Each of these factors could contribute to the discrepancy observed between theoretical calculations and actual experimental results. Analyzing these errors helps refine methodologies, improve accuracy in future experiments, and ensure that your conclusions are robust and reliable. Understanding and minimizing sources of error are as crucial as understanding concepts like stoichiometry and gas laws.

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Most popular questions from this chapter

The label has come off a cylinder of gas in your laboratory. You know only that one species of gas is contained in the cylinder, but you do not know whether it is hydrogen, oxygen, or nitrogen. To find out, you evacuate a 5 -liter flask, seal it and weigh it, then let gas from the cylinder flow into it until the gauge pressure equals 1.00 atm. The flask is reweighed, and the mass of the added gas is found to be 13.0g. Room temperature is \(27^{\circ} \mathrm{C}\), and barometric pressure is 1.00 atm. What is the gas?

A process stream flowing at \(35 \mathrm{kmol} / \mathrm{h}\) contains 15 mole \(\%\) hydrogen and the remainder 1 -butene. The stream pressure is 10.0 atm absolute, the temperature is \(50^{\circ} \mathrm{C}\), and the velocity is \(150 \mathrm{m} / \mathrm{min}\). Determine the diameter (in \(\mathrm{cm}\) ) of the pipe transporting this stream, using Kay's rule in your calculations.

The demand for a particular hydrogenated compound, \(\mathrm{S}\), is \(5.00 \mathrm{kmol} / \mathrm{h}\). This chemical is synthesized in the gas-phase reaction $$A+H_{2}=S$$ The reaction equilibrium constant at the reactor operating temperature is $$K_{p}=\frac{p_{\mathrm{S}}}{p_{\Lambda} p_{\mathrm{H}_{2}}}=0.1 \mathrm{atm}^{-1}$$ The fresh feed to the process is a mixture of \(A\) and hydrogen that is mixed with a recycle stream consisting of the same two species. The resulting mixture, which contains \(3 \mathrm{kmol} \mathrm{A} / \mathrm{kmol} \mathrm{H}_{2},\) is fed to the reactor, which operates at an absolute pressure of 10.0 atm. The reaction products are in equilibrium. The effluent from the reactor is sent to a separation unit that recovers all of the \(S\) in essentially pure form. The A and hydrogen leaving the separation unit form the recycle that is mixed with fresh feed to the process. Calculate the feed rates of hydrogen and A to the process in kmol/h and the recycle stream flow rate in SCMH (standard cubic meters per hour).

Oxygen therapy uses various devices to provide oxygen to patients having difficulty getting sufficient amounts from air through normal breathing. Among the devices is a nasal cannula, which transports oxygen through small plastic tubes from a supply tank to prongs placed in the nostril. Consider a specific configuration in which the supply tank, whose volume is \(6.0 \mathrm{ft}^{3},\) is filled to a pressure of 2100 psig at a temperature of \(85^{\circ} \mathrm{F}\). The paticnt is in an environment where the ambicnt temperature is \(40^{\circ} \mathrm{F}\). When the cannula is put into use, the pressure in the tank begins to decrease as oxygen flows at \(10-15 \mathrm{L} / \mathrm{min}\) through a tube and the cannula into the nostrils. (a) Estimate the original mass of oxygen in the tank using the compressibility-factor equation of state. (b) What is the initial pressure when the temperature is 40 \(^{\circ} \mathrm{F} ?\) How much oxygen remains in the tank when application of the ideal-gas equation of state produces a result that is within \(3 \%\) of that predicted by the compressibility-factor equation of state (i.e., when \(0.97 \leq z \leq 1.03\) )? (c) How long will it take for the gauge on the tank to read 50 psig, assuming an average flow rate of \(12.5 \mathrm{L} / \mathrm{min} ?\)

Air in industrial plants is subject to contamination by many different chemicals, and companies must monitor ambient levels of hazardous species to be sure they are below limits specified by the National Institute for Occupational Safety and Health (NIOSH). In personal breathing-zone sampling (as opposed to area sampling), workers wear devices that periodically collect air samples less than 10 inches away from their noses. Breathing-zone sampling and analysis methods for hundreds of species are set forth in the NIOSH Manual of Analytical Methods. \(^{13}\) For benzene, NIOSH specifies a recommended exposure limit (REL) of 0.1 ppm time-weighted average exposure (TWA), and the Occupational Safety and Health Administration (OSHA) permissible exposure limit (PEL) is 1.0ppm TWA. A worker in a petrolcum refinery has a personal breathing-zone sampler for benzenc clipped to her shirt collar. Following the NIOSH prescription, air is pumped through the sampler at a rate of \(0.200 \mathrm{L} / \mathrm{min}\) by a small battery-operated pump attached to the worker's belt. The sampler contains an adsorbent that removes essentially all of the benzene from the air passing through it. After several hours, the sampler is removed and sent to a lab for analysis, and the worker puts on a fresh sampler. On a particular day when the temperature is \(21^{\circ} \mathrm{C}\) and barometric pressure is \(730 \mathrm{mm}\) Hg, samples are collected during a 4-h period before lunch and a 3.5-h period after lunch. The analytical laboratory reports \(0.17 \mathrm{mg}\) of benzene in the first sample and \(0.23 \mathrm{mg}\) in the second. (a) Calculate the average benzene concentration, \(C_{\mathrm{B}}(\mathrm{ppm}),\) in the worker's breathing zone during each sampling period, where 1 ppm = 1 mol C \(_{6} \mathrm{H}_{6} / 10^{6}\) mol air. (b) The worker's TWA is the average concentration of benzene in her breathing zone during the eight hours of her shift. It is calculated by multiplying \(C_{\mathrm{B}}\) in each sampling period by the time of that period, summing the products over all periods during the shift, and dividing by the total time of the shift. Assume that the worker's exposure during the unsampled 30 minutes was zero, and calculate her TWA. (c) If the worker's exposure is above the recommended limits, what actions might the company take?
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