Which statement correctly describes Dalton's Law for partial pressures in a gas mixture?

Which statement correctly describes Dalton's Law for partial pressures in a gas mixture?

• A. Partial pressure of a gas in a mixture equals the total pressure of the mixture multiplied by the number of gas molecules
• B. Partial pressure of a gas in a mixture equals its mole fraction times the total pressure
• C. Partial pressure of a gas in a mixture equals the sum of the pressures of the other gases
• D. Partial pressure of a gas in a mixture equals the atmospheric pressure

Answer: (B)

In a gas mixture, each component contributes to the total pressure in proportion to how much of the gas is present. The fraction of molecules that are a given gas is its mole fraction, xi. Dalton’s Law tells us that the partial pressure Pi of that gas is its mole fraction times the total pressure Ptot: Pi = xi × Ptot. This means the share of the total pressure that a gas exerts is determined by how prevalent it is in the mixture, not by the absolute number of molecules alone. For example, if the total pressure is 2 atm and a gas makes up 0.25 of the molecules, its partial pressure is 0.25 × 2 atm = 0.5 atm. The total pressure is the sum of all such partial pressures. The other ideas don’t fit because pressure isn’t determined by simply multiplying by the number of molecules, nor is a gas’s partial pressure the sum of the pressures of the others, and it isn’t fixed to atmospheric pressure unless the total pressure and composition happen to line up that way.

In a gas mixture, each component contributes to the total pressure in proportion to how much of the gas is present. The fraction of molecules that are a given gas is its mole fraction, xi. Dalton’s Law tells us that the partial pressure Pi of that gas is its mole fraction times the total pressure Ptot: Pi = xi × Ptot. This means the share of the total pressure that a gas exerts is determined by how prevalent it is in the mixture, not by the absolute number of molecules alone.

For example, if the total pressure is 2 atm and a gas makes up 0.25 of the molecules, its partial pressure is 0.25 × 2 atm = 0.5 atm. The total pressure is the sum of all such partial pressures.

The other ideas don’t fit because pressure isn’t determined by simply multiplying by the number of molecules, nor is a gas’s partial pressure the sum of the pressures of the others, and it isn’t fixed to atmospheric pressure unless the total pressure and composition happen to line up that way.