(b) What is the concentration of neon in the atmosphere in molecules per liter, assuming an atmospheric pressure of 730 torr and a temperature of 296 K?

Verified step by step guidance

Step 1: Convert the atmospheric pressure from torr to atm. Use the conversion factor: 1 atm = 760 torr.

Step 2: Use the Ideal Gas Law equation, PV = nRT, to find the number of moles of neon per liter. Here, P is the pressure in atm, V is the volume in liters (1 L for simplicity), n is the number of moles, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin.

Step 3: Rearrange the Ideal Gas Law equation to solve for n (moles of gas): n = PV / RT.

Step 4: Calculate the number of moles of neon using the values from Step 1 and the given temperature.

Step 5: Convert the moles of neon to molecules using Avogadro's number (6.022 x 10^23 molecules/mol) to find the concentration of neon in molecules per liter.

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 a 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. This law allows us to calculate the concentration of gases under specific conditions.

Molar Volume of a Gas

At standard temperature and pressure (STP), one mole of an ideal gas occupies 22.4 liters. However, under different conditions, such as varying pressure and temperature, the volume occupied by a mole of gas changes. Understanding how to adjust for these conditions is crucial for calculating the concentration of gases in the atmosphere.

Concentration in Molecules per Liter

Concentration can be expressed in various units, including moles per liter (M) or molecules per liter. To convert from moles to molecules, Avogadro's number (approximately 6.022 x 10^23 molecules per mole) is used. This conversion is essential for determining the number of gas molecules present in a given volume, particularly in atmospheric chemistry.

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