/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 15 The label has come off a cylinde... [FREE SOLUTION] | 91Ó°ÊÓ

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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?

Short Answer

Expert verified
The gas in the cylinder is oxygen.

Step by step solution

01

Convert the temperature from Celsius to Kelvin

To conduct any gas law calculations, the temperature must be expressed in Kelvin (K). The conversion from Celsius to Kelvin is done by adding 273 to the Celsius temperature. Thus, \(27^\circ C = 300 K\).
02

Calculate the moles of the gas

Use the Ideal Gas Law \(PV = nRT\) where P = 1 atm, V = 5 L, R = 0.0821 L·atm/K·mol (ideal gas constant), and T = 300 K to calculate the number of moles (n). It is rearranged to \( n = PV/RT \) to find that \( n = (1 atm · 5 L)/(0.0821 L·atm/K·mol · 300K) = 0.203 mol \)
03

Calculate the molar mass of the gas

The molar mass (MW) of a substance is its mass (g) divided by the amount (mol). Therefore the molar mass of the gas (g/mol) = mass of the gas (g) ÷ amount of the gas (mol). This gives \( MW = 13.0 g / 0.203 mol = 64.0 g/mol \)
04

Identify the gas

The calculated molar mass (64.0 g/mol) is compared to the molar masses of hydrogen (~1 g/mol), oxygen (~32 g/mol), and nitrogen (~28 g/mol). The molar mass closest to the calculated one is oxygen, so the gas in the cylinder is most likely oxygen.

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Key Concepts

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

Gas Identification
Identifying an unknown gas in a laboratory setting can be accomplished using the Ideal Gas Law and information about the gas' properties. In the given exercise, we are presented with three possible gases: hydrogen, oxygen, and nitrogen. Each of these gases has a unique molar mass. By comparing the molar mass calculated from the experiment with the known molar masses of potential gases, we can make an educated guess about the gas' identity. In this context, the molar mass acts as a 'fingerprint' for chemical substances, allowing for accurate identification when measured precisely.

Understanding how to calculate and compare molar masses is essential in chemistry, not only for identification but also for stoichiometry and reaction prediction. The process involves a careful balance of measurement, calculation, and comparison against established data.
Molar Mass Calculation
Molar mass is defined as the mass of one mole of a substance and is expressed in grams per mole (g/mol). To calculate the molar mass of a gas from experimental data, you need to know the mass of a known volume of the gas at a specified temperature and pressure - precisely the information provided in the exercise. After determining the amount of gas (in moles) using the Ideal Gas Law, the next step is to divide the measured gas mass by the number of moles to find the molar mass.

This calculated molar mass can be utilized as a crucial parameter in various chemical calculations, such as determining the formula of a compound, finding the percent composition, or converting between mass and moles in a chemical reaction.
Gas Law Calculations
Gas Law calculations involve equations that relate the pressure, volume, temperature, and number of moles of a gas. In the exercise, we used the Ideal Gas Law, which is the cornerstone of gas law calculations. The flexibility of this equation allows us to solve for any one of the variables if the other three are known. This versatile formula is essential for various applications in both chemistry and physics, from calculating the behavior of gases in different environmental conditions to understanding the thermodynamics of gaseous systems.

By mastering gas law calculations, students can confidently approach a variety of real-world problems that involve gases and their interactions. The key is to ensure all units match the Ideal Gas Law's requirements, especially with temperature in Kelvin and pressure in atmospheres, for consistency and accuracy.
PV=nRT
The equation PV=nRT, known as the Ideal Gas Law, provides a mathematical relationship between the pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T) of an ideal gas. This law is the culmination of Boyle's Law, Charles's Law, Avogadro's Law, and Gay-Lussac's Law, and it assumes that the particles of an ideal gas do not attract or repel each other and take up no space. Though no gas is perfectly ideal, the Ideal Gas Law gives a close approximation for many gases under standard conditions.

By comprehending how to manipulate the Ideal Gas Law and solve for any of its individual components, students can explore varied gas-related scenarios, from the expansion of a balloon to the kinetics of a chemical reaction involving gases. The gas constant (R) used must match the units of pressure, volume, and temperature within the context of the problem.
Temperature Conversion
Temperature conversion in gas law calculations is critical because the laws on which these calculations are based—such as Charles's Law and Gay-Lussac's Law—are derived from experiments where temperature is measured on an absolute scale (Kelvin scale). To ensure accuracy in gas law problems, it's essential always to convert temperature from Celsius or Fahrenheit to Kelvin.

The conversion from Celsius to Kelvin is straightforward: simply add 273.15 to the Celsius temperature. For Fahrenheit, the conversion involves subtracting 32, then multiplying by 5/9, and finally adding 273.15. These conversions are critical because the volume and pressure of gases are directly related to their temperature in Kelvin, which means accurate temperature data is necessary for reliable gas behaviors predictions.

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Most popular questions from this chapter

A tank in a room at \(19^{\circ} \mathrm{C}\) is initially open to the atmosphere on a day when the barometric pressure is 102 kPa. A block of dry ice (solid \(\mathrm{CO}_{2}\) ) with a mass of \(15.7 \mathrm{kg}\) is dropped into the tank, which is then sealed. The reading on the tank pressure gauge initially rises very quickly, then much more slowly, eventually reaching a value of 3.27 MPa. Assume \(T_{\text {final }}=19^{\circ} \mathrm{C}\) (a) How many moles of air were in the tank initially? Neglect the volume occupied by \(\mathrm{CO}_{2}\) in the solid state, and assume that a negligible amount of \(\mathrm{CO}_{2}\) escapes prior to the sealing of the tank. (b) Estimate the percentage error made by neglecting the volume of the block of dry ice placed in the tank. (The specific gravity of solid carbon dioxide is approximately 1.56 .) (c) What is the final density (g/L) of the gas in the tank? (d) Explain the observed variation of pressure with time. More specifically, what is happening in the tank during the initial rapid pressure increase and during the later slow pressure increase?

A nitrogen rotameter is calibrated by feeding \(\mathrm{N}_{2}\) from a compressor through a pressure regulator, a needle valve, the rotameter, and a dry test meter, a device that measures the total volume of gas that passes through it. A water manometer is used to measure the gas pressure at the rotameter outlet. A flow rate is set using the needle valve, the rotameter reading, \(\phi\), is noted, and the change in the dry gas meter reading \((\Delta V)\) for a measured running time \((\Delta t)\) is recorded. The following calibration data are taken on a day when the temperature is \(23^{\circ} \mathrm{C}\) and barometric pressure is \(763 \mathrm{mm} \mathrm{Hg} .\) $$\begin{array}{rrr} \hline \phi & \Delta t(\min ) & \Delta V(\mathrm{L}) \\ \hline 5.0 & 10.0 & 1.50 \\ 9.0 & 10.0 & 2.90 \\ 12.0 & 5.0 & 2.00 \\ \hline \end{array}$$ (a) Prepare a calibration chart of \(\phi\) versus \(\dot{V}_{\text {sid }}\), the flow rate in standard \(\mathrm{cm}^{3} / \mathrm{min}\) equivalent to the actual flow rate at the measurement conditions. (b) Suppose the rotameter-valve combination is to be used to set the flow rate to 0.010 mol \(\mathrm{N}_{2} / \mathrm{min}\). What rotameter reading must be maintained by adjusting the valve?

After being purged with nitrogen, a low-pressure tank used to store flammable liquids is at a total pressure of 0.03 psig. (a) If the purging process is done in the moming when the tank and its contents are at \(55^{\circ} \mathrm{F}\), what will be the pressure in the tank when it is at \(85^{\circ} \mathrm{F}\) in the afternoon? (b) If the maximum design gauge pressure of the tank is 8 inches of water, has the design pressure been exceeded? (c) Speculate on the purpose of purging the tank with nitrogen.

A stream of oxygen enters a compressor at \(298 \mathrm{K}\) and 1.00 atm at a rate of \(127 \mathrm{m}^{3} / \mathrm{h}\) and is compressed to \(358 \mathrm{K}\) and 1000 atm. Estimate the volumetric flow rate of compressed \(\mathrm{O}_{2},\) using the compressibility-factor equation of state.

Phosgene (CCl, O) is a colorless gas that was used as an agent of chemical warfare in World War I. It has the odor of new-mown hay (which is a good warning if you know the smell of new-mown hay). Pete Brouillette, an innovative chemical engincering student, came up with what he believed was an effective new process that utilized phosgene as a starting material. He immediately set up a reactor and a system for analyzing the reaction mixture with a gas chromatograph. To calibrate the chromatograph (i.e., to determine its response to a known quantity of phosgene), he evacuated a 15.0 cm length of tubing with an outside diameter of \(0.635 \mathrm{cm}\) and a wall thickness of \(0.559 \mathrm{mm}\), and then connected the tube to the outlet valve of a cylinder containing pure phosgene. The idea was to crack the valve, fill the tube with phosgene, close the valve, feed the tube contents into the chromatograph, and observe the instrument response. What Pete hadn't thought about (among other things) was that the phosgene was stored in the cylinder at a pressure high enough for it to be a liquid. When he opened the cylinder valve, the liquid rapidly flowed into the tube and filled it. Now he was stuck with a tube full of liquid phosgene at a pressure the tube was not designed to support. Within a minute he was reminded of a tractor ride his father had once given him through a hayfield, and he knew that the phosgene was leaking. He quickly ran out of the lab, called campus security, and told them that a toxic leak had occurred, that the building had to be evacuated, and the tube removed and disposed of properly. Personnel in air masks shortly appeared, took care of the problem, and then began an investigation that is still continuing. (a) Show why one of the reasons phosgene was an effective weapon is that it would collect in low spots soldiers often mistakenly entered for protection. (b) Pete's intention was to let the tube equilibrate at room temperature ( \(23^{\circ} \mathrm{C}\) ) and atmospheric pressure. How many gram-moles of phosgene would have been contained in the sample fed to the chromatograph if his plan had worked? (c) The laboratory in which Pete was working had a volume of \(2200 \mathrm{ft}^{3}\), the specific gravity of liquid phosgene is \(1.37,\) and Pete had read somewhere that the maximum "safe" concentration of phosgene in air is \(0.1 \mathrm{ppm}\) \(\left(0.1 \times 10^{-6} \mathrm{mol} \mathrm{CCl}_{2} \mathrm{O} / \mathrm{mol}\) air) \right. Would the "safe" concentration have been exceeded if all the liquid phosgene in the tube had evaporated into the room? Even if the limit would not have been exceeded, give several reasons why the lab would still have been unsafe. (d) List several things Pete did (or failed to do) that made his experiment unnecessarily hazardous.

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