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Chapter 5: Problem 28

Write the ideal gas equation and also state it in words. Give the units for each term in the equation.

Short Answer

Expert verified
The ideal gas equation is \( PV = nRT \). In words, this reads: the product of the pressure and volume of a gas is equal to the number of moles of the gas multiplied by the gas constant multiplied by the temperature. The units are: Pressure(P) in Pascal (Pa), Volume(V) in cubic meters (m³), number of moles (n) in mol, gas constant (R) in J.mol⁻¹.K⁻¹, temperature (T) in Kelvin.

Step by step solution

01

- Write down the ideal gas equation

The ideal gas equation is usually represented by \( PV = nRT \), where:\n P = Pressure,\n V = Volume,\n n = number of moles,\n R = ideal gas constant,\n T = temperature
02

- Express the equation in words

In words, this equation states: the product of the pressure and volume of an ideal gas is equal to the number of moles of the gas multiplied by the gas constant and the temperature.
03

- Identify the units for each term

In the International System unit:\n\n- The unit of pressure P is Pascal (Pa),\n- Volume V is typically expressed in cubic meters (m³),\n- Number of moles n is dimensionless but often expressed in moles (mol),\n- The universal gas constant R is given in J.mol⁻¹.K⁻¹ (Joules per mole per Kelvin),\n- The temperature T is expressed in Kelvin (K).

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Most popular questions from this chapter

A \(36.4-\mathrm{L}\) volume of methane gas is heated from \(25^{\circ} \mathrm{C}\) to \(88^{\circ} \mathrm{C}\) at constant pressure. What is the final volume of the gas?

Is the atmospheric pressure in a mine that is \(500 \mathrm{~m}\) below sea level greater or less than 1 atm?

Dry air near sea level has the following composition by volume: \(\mathrm{N}_{2}, 78.08\) percent; \(\mathrm{O}_{2}, 20.94\) percent; \(\mathrm{Ar},\) 0.93 percent; \(\mathrm{CO}_{2}, 0.05\) percent. The atmospheric pressure is \(1.00 \mathrm{~atm} .\) Calculate (a) the partial pressure of each gas in atm and (b) the concentration of each gas in moles per liter at \(0^{\circ} \mathrm{C}\).

The volume of a sample of pure HCl gas was \(189 \mathrm{~mL}\) at \(25^{\circ} \mathrm{C}\) and \(108 \mathrm{mmHg}\). It was completely dissolved in about \(60 \mathrm{~mL}\) of water and titrated with an \(\mathrm{NaOH}\) solution; \(15.7 \mathrm{~mL}\) of the \(\mathrm{NaOH}\) solution were required to neutralize the \(\mathrm{HCl}\). Calculate the molarity of the \(\mathrm{NaOH}\) solution.

Apply your knowledge of the kinetic theory of gases to these situations. (a) Does a single molecule have a temperature? (b) Two flasks of volumes \(V_{1}\) and \(V_{2}\left(V_{2}>V_{1}\right)\) contain the same number of helium atoms at the same temperature. (i) Compare the root- mean-square (rms) speeds and average kinetic energies of the helium (He) atoms in the flasks. (ii) Compare the frequency and the force with which the He atoms collide with the walls of their containers (c) Equal numbers of He atoms are placed in two flasks of the same volume at temperatures \(T_{1}\) and \(T_{2}\left(T_{2}>T_{1}\right)\) (i) Compare the rms speeds of the atoms in the two flasks. (ii) Compare the frequency and the force with which the He atoms collide with the walls of their containers. (d) Equal numbers of He and neon (Ne) atoms are placed in two flasks of the same volume and the temperature of both gases is \(74^{\circ} \mathrm{C}\). Comment on the validity of these statements: (i) The rms speed of He is equal to that of Ne. (ii) The average kinetic energies of the two gases are equal. (iii) The rms speed of each He atom is \(1.47 \times 10^{3} \mathrm{~m} / \mathrm{s}\).
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