If the pressure exerted by ozone, O3, in the stratosphere is 3.0×10−3atm and the temperature is 250 K, how many ozone molecules are in a liter?

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Identify the given values: Pressure (P) = 3.0×10−3 atm, Temperature (T) = 250 K, and Volume (V) = 1 L.

Use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant (0.0821 L atm K−1 mol−1), and T is the temperature.

Rearrange the ideal gas law equation to solve for n (number of moles of gas): n = \(\frac{PV}{RT}\).

Calculate the number of moles of ozone using the values of P, V, R, and T substituted into the rearranged ideal gas law equation.

Convert the number of moles of ozone to number of molecules by using Avogadro's number (6.022×10^23 molecules/mol). Multiply the number of moles by Avogadro's number to find the total number of ozone molecules in 1 liter.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. In this context, P is the pressure of ozone, V is the volume (1 liter), n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. This law allows us to calculate the number of molecules present in a given volume of gas under specific conditions.

Avogadro's Number

Avogadro's Number, approximately 6.022 × 10²³, is the number of particles (atoms, molecules, etc.) in one mole of a substance. This concept is crucial for converting between moles and molecules. Once we determine the number of moles of ozone using the Ideal Gas Law, we can multiply by Avogadro's Number to find the total number of ozone molecules in the specified volume.

Gas Pressure and Temperature Relationship

Gas pressure is influenced by temperature, as described by the kinetic molecular theory. Higher temperatures increase the kinetic energy of gas molecules, leading to higher pressure if the volume is constant. In this problem, understanding how pressure and temperature interact is essential for applying the Ideal Gas Law correctly to find the number of ozone molecules at the given conditions.