A certain nonmetal reacts with hydrogen at 440 °C to form a poisonous, foul-smelling gas. A sample with a mass of 6.618 g was found to have a volume of 2.00 L at 25.0 °C and 1.00 atm. What is the molecular weight of the gas? (LO 10.6) (a) 67.9 g/mol (b) 162 g/mol (c) 80.9 g/mol (d) 193.6 g/mol

Verified step by step guidance

Step 1: Use the Ideal Gas Law to find the number of moles of the gas. 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 temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. This will give you the temperature in Kelvin needed for the Ideal Gas Law calculation.

Step 3: Rearrange the Ideal Gas Law equation to solve for n (number of moles): n = PV / RT. Substitute the given values for P (1.00 atm), V (2.00 L), R (0.0821 L·atm/mol·K), and T (temperature in Kelvin) into the equation.

Step 4: Calculate the number of moles using the rearranged Ideal Gas Law equation. This will give you the amount of gas in moles present in the sample.

Step 5: Determine the molecular weight of the gas by dividing the mass of the gas sample (6.618 g) by the number of moles calculated in the previous step. This will give you the molecular weight in g/mol.

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. Here, 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 is essential for calculating the number of moles of the gas from the given conditions, which is necessary for determining its molecular weight.

Molecular Weight

Molecular weight, or molar mass, is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It can be calculated by dividing the mass of the gas sample by the number of moles obtained from the Ideal Gas Law. Understanding how to calculate molecular weight is crucial for identifying the correct answer among the provided options.

Gas Properties and Conditions

Gas properties are influenced by temperature, pressure, and volume, which can change the behavior of gases. In this question, the gas is measured at specific conditions (25.0 °C and 1.00 atm), which are standard for calculations. Recognizing how these conditions affect gas behavior is vital for applying the Ideal Gas Law correctly and obtaining accurate results.

Recommended video:

Guided course