What are the units of the unknown quantity for the following problem? Calculate the molar mass of oxygen gas given that 1.00 g of gas occupies 0.700 L.

Question

Quizplus · Accepted Answer

The molar mass of a substance is the mass of one mole of its entities (atoms, molecules or formula units). Therefore, the units of molar mass are grams per mole (g/mol). In this problem, we are given the mass (1.00 g) and volume (0.700 L) of a gas, but we need to find its molar mass. We can use the ideal gas law and the relationship between molar mass, mass and volume to solve for the unknown quantity:

PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

Assuming constant temperature and pressure, we can rearrange the equation to solve for n/V (molarity):

n/V = P/(RT)

We can then use the definition of molarity and the mass given in the problem to solve for the molar mass (M):

M = m/(n/V) = m(RT/P)V

We are given m = 1.00 g and V = 0.700 L, and we can assume T and P are constant (at standard temperature and pressure, for example). The gas constant R is 0.0821 L⋅atm/(mol⋅K). Therefore, we have:

M = (1.00 g) (0.0821 L⋅atm/(mol⋅K)) (273 K)/(1 atm) (0.700 L)

M = 32.0 g/mol

The units of M are g/mol, which is choice (C).

What Are the Units of the Unknown Quantity for the Following