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Ch 18: Thermal Properties of Matter
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo
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Capitolo 18, Problema 25

In a gas at standard conditions, what is the length of the side of a cube that contains a number of molecules equal to the population of the earth (about 7×1097\(\times\)10^9 people)?

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First, understand that the problem involves calculating the volume of a cube that contains a specific number of molecules, equivalent to the population of the Earth, which is approximately 7 * 10^9 molecules.
Next, recall that at standard conditions (0°C and 1 atm), one mole of an ideal gas occupies 22.4 liters. Use Avogadro's number, which is approximately 6.022 * 10^23 molecules per mole, to find the volume occupied by 7 * 10^9 molecules.
Calculate the number of moles corresponding to 7 * 10^9 molecules using the formula: \( \text{Number of moles} = \frac{\text{Number of molecules}}{\text{Avogadro's number}} \).
Determine the volume occupied by these moles using the relation: \( \text{Volume} = \text{Number of moles} \times 22.4 \text{ liters/mole} \).
Finally, find the length of the side of the cube by taking the cube root of the volume in liters, since the volume of a cube is given by \( \text{Volume} = \text{side length}^3 \).

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Avogadro's Number

Avogadro's Number is a fundamental constant in chemistry and physics, representing the number of constituent particles, usually atoms or molecules, in one mole of a substance. It is approximately 6.022 x 10^23 particles per mole. This concept is crucial for converting between the number of molecules and moles, which is necessary for calculating the volume of gas containing a specific number of molecules.
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Moles & Avogadro's Number

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in physics that relates the pressure, volume, temperature, and number of moles of an ideal gas. It is expressed as 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. This law helps determine the volume occupied by a given number of molecules under standard conditions.
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Standard Conditions

Standard conditions refer to a set of agreed-upon reference conditions for temperature and pressure used in scientific calculations. Typically, these are 0°C (273.15 K) and 1 atm pressure. Understanding standard conditions is essential for applying the Ideal Gas Law to find the volume of a gas, as it provides a baseline for calculations involving gases.
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