(d) If you measure pressure in bars instead of atmospheres, calculate the corresponding value of R in L-bar/mol-K.

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Identify the value of the gas constant (R) in the original unit, which is typically given in L-atm/mol-K. The common value used is R = 0.0821 L-atm/mol-K.

Understand the conversion factor between atmospheres and bars. 1 atm is approximately equal to 1.01325 bars.

Set up the conversion equation to find the new R value in L-bar/mol-K. Use the formula: R_{new} = R_{old} \times \frac{1 \, \text{atm}}{1.01325 \, \text{bars}}.

Substitute the known values into the conversion equation. Replace R_{old} with 0.0821 L-atm/mol-K and the conversion factor.

Calculate the new value of R in L-bar/mol-K by performing the multiplication. This will give you the value of R when pressure is measured in bars instead of atmospheres.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of an ideal gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. Understanding this law is essential for manipulating gas properties and converting between different units of pressure.

Units of Pressure

Pressure can be measured in various units, including atmospheres (atm), bars, and pascals (Pa). One bar is defined as 100,000 pascals, and 1 atm is approximately equal to 1.01325 bars. When converting the ideal gas constant R to different units, it is crucial to understand these relationships to ensure accurate calculations and conversions.

Ideal Gas Constant (R)

The ideal gas constant R is a proportionality constant in the Ideal Gas Law that relates the energy scale to the temperature scale. Its value varies depending on the units used for pressure, volume, and temperature. For example, R = 0.08314 L·bar/(mol·K) when pressure is measured in bars, which is necessary for calculations involving gases under different conditions.

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Textbook Question

(a) Amonton's law expresses the relationship between pressure and temperature. Use Charles's law and Boyle's law to derive the proportionality relationship between P and T.

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Textbook Question

(b) What is the molar volume of an ideal gas at STP?

Textbook Question

Suppose you are given two 1-L flasks and told that one contains a gas of molar mass 30 and the other a gas of molar mass 60, both at the same temperature. The pressure in flask A is x atm, and the mass of gas in the flask is 1.2 g. The pressure in flask B is 0.5x atm, and the mass of gas in that flask is 1.2 g. Which flask contains the gas of molar mass 30, and which contains the gas of molar mass 60?

Textbook Question

Suppose you are given two flasks at the same temperature, one of volume 2 L and the other of volume 3 L. The 2-L flask contains 4.8 g of gas, and the gas pressure is x atm. The 3-L flask contains 0.36 g of gas, and the gas pressure is 0.1x. Do the two gases have the same molar mass? If not, which contains the gas of higher molar mass?

Textbook Question

Complete the following table for an ideal gas: