Problem 71 - Chemistry Matter and Change

Question

Find the volume that 42 g of carbon monoxide gas occupies at STP.

Step-by-Step Solution

Answer

The volume that 42 g of carbon monoxide gas occupies at STP is approximately 34.0 liters when using the ideal gas law and considering 1.5 moles of CO in the given mass.

Step 1: Calculate the number of moles of the carbon monoxide gas

To calculate the number of moles of carbon monoxide, we will use the given mass (42 g) and the molar mass of CO (28 g/mol). n = mass/molar_mass = 42 g / 28 g/mol = 1.5 mol Thus, there are 1.5 moles of carbon monoxide gas.

Step 2: Use the ideal gas law to find the volume

Knowing the number of moles, we can use the ideal gas law formula (PV = nRT) and the STP conditions (P = 1 atm, T = 273 K) to solve for the volume (V). PV = nRT -> V = nRT/P Substituting the known values into the equation, we have: V = (1.5 mol) * (0.0821 L*atm/mol*K) * (273 K) / (1 atm) V = 33.9957 L

Step 3: Round your solution

To present the final answer, we will round the volume value to an appropriate number of significant figures. V ≈ 34.0 L The volume that 42 g of carbon monoxide gas occupies at STP is approximately 34.0 liters.

Key Concepts

Molar Mass

Molar mass is a fundamental concept in chemistry, referring to the mass of one mole of a given substance. It is typically expressed in grams per mole (g/mol). To determine the molar mass of a compound, add up the atomic masses of all the atoms within a molecule of the substance. Atomic masses can be found on the periodic table next to each element symbol.

In the context of the original exercise, carbon monoxide (CO) is comprised of one atom of carbon and one atom of oxygen. The atomic mass of carbon is about 12 grams/mole and for oxygen, it is about 16 grams/mole. When these are combined, the molar mass for carbon monoxide is 28 grams/mole. This molar mass allows us to calculate the number of moles in a given sample when given the sample's total mass. For instance, in the problem, 42 grams of CO is divided by its molar mass, 28 g/mol, resulting in 1.5 moles of CO.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) are conditions often used as a reference point in gas law calculations. They are defined as a temperature of 273.15 K (0°C) and a pressure of 1 atm. These specific conditions simplify calculations for gases because they provide a common standard.

STP is important when using the ideal gas law, which helps determine the relationship between pressure, volume, temperature, and the number of moles in a gas. Under these conditions, one mole of an ideal gas occupies a volume of 22.4 liters. It is crucial to note that the behavior of real gases can slightly deviate from this ideal due to various factors like intermolecular forces and the actual volume occupied by the gas molecules themselves.

Volume Calculation

Volume calculation of gases often involves using the ideal gas law, which is expressed as PV = nRT. Here:

• P is the pressure
• V is the volume
• n is the number of moles
• R is the ideal gas constant, 0.0821 L*atm/mol*K
• T is the temperature in Kelvin

To find the volume of a gas at STP, rearrange this formula to solve for V, giving V = nRT/P. After determining the number of moles and knowing the conditions at STP, plug these values into this equation.

In the exercise, the number of moles is 1.5, the constant R is 0.0821 L*atm/mol*K, the temperature at STP is 273 K, and the pressure is 1 atm. Therefore, the calculation is V = (1.5 mol) * (0.0821 L*atm/mol*K) * (273 K) / (1 atm), yielding approximately 34.0 liters as the volume of carbon monoxide gas.

Chemical Stoichiometry

Chemical stoichiometry involves the calculation of the quantities of reactants and products in chemical reactions. It is based on the laws of conservation of mass and moles, which ensure that in a balanced chemical equation, the number of atoms for each element is the same on both sides of the equation.

In gas-related problems, stoichiometry helps in predicting the volumes, pressures, and temperatures of the gases involved when you know other conditions about the chemical reaction or the state of the gas.

In the provided exercise, stoichiometry is used indirectly to relate the mass of carbon monoxide to its moles, which are then used to determine the volume. By understanding stoichiometry, you can efficiently navigate through chemical conversions and understand the underlying principles governing reactions and behaviors of gases.