Which sample contains more molecules, 3.14 L of Ar at 85.0 °C and 1111 mm Hg pressure or 11.07 g of Cl₂?

Verified step by step guidance

Step 1: Use the ideal gas law to calculate the number of moles of Ar. The ideal gas law is given by the equation 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.

Step 2: Convert the given pressure from mm Hg to atm, as the ideal gas constant R is typically used with pressure in atm. Use the conversion factor 1 atm = 760 mm Hg.

Step 3: Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature.

Step 4: Rearrange the ideal gas law equation to solve for n (number of moles): n = PV / RT. Substitute the values for P, V, R, and T to find the moles of Ar.

Step 5: Calculate the number of moles of Cl₂ using its molar mass. The molar mass of Cl₂ is approximately 70.90 g/mol. Divide the given mass of Cl₂ by its molar mass to find the moles of Cl₂.

Key Concepts

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

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law allows us to calculate the number of moles (n) of a gas when we know its pressure (P), volume (V), and temperature (T). Understanding this concept is essential for comparing the number of molecules in different gas samples.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For example, the molar mass of Cl₂ is approximately 70.9 g/mol. Knowing the molar mass allows us to convert between grams of a substance and the number of moles, which is crucial for determining how many molecules are present in a given mass.

Avogadro's Number

Avogadro's Number, approximately 6.022 x 10²³, is the number of molecules in one mole of a substance. This constant is fundamental in chemistry for converting between moles and molecules. By using Avogadro's Number, we can easily find the total number of molecules in a sample once we have calculated the number of moles.

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