Question

Помогите решить задачу.сколько молекул воздуха содержится в аудитори,имеющей форму прямоугольного параллепипеда с высотой 3 м, шириной 5 м и длинной 15 м, если молярная масса воздуха 29*10^-3 кг/моль?

Answer 1

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Answer 2

Calculating the Number of Air Molecules in the Room

To calculate the number of air molecules in the room, we can use the following steps:

1. Calculate the Volume of the Room: - The volume of a rectangular parallelepiped (a box-shaped room) can be calculated using the formula: volume = length * width * height.

2. Convert the Volume to Cubic Meters: - Ensure that the dimensions of the room are in meters to match the units of the molar mass of air.

3. Calculate the Number of Moles of Air: - Use the formula: moles = mass / molar mass.

4. Convert Moles to Molecules: - Use Avogadro's number, which is approximately 6.022 x 10^23 molecules per mole, to convert moles to molecules.

Let's proceed with these calculations.

Calculation Steps

1. Calculate the Volume of the Room: - Given: - Height (h) = 3 m - Width (w) = 5 m - Length (l) = 15 m - Using the formula: volume = length * width * height - Calculating: volume = 15 m * 5 m * 3 m = 225 m³

2. Convert the Volume to Cubic Meters: - The volume of the room is already in cubic meters.

3. Calculate the Number of Moles of Air: - Given: - Molar mass of air = 29 * 10^-3 kg/mol - Using the formula: moles = mass / molar mass - Assuming the mass of the air in the room is negligible, we can calculate the moles directly.

4. Convert Moles to Molecules: - Using Avogadro's number: 1 mole = 6.022 x 10^23 molecules

Final Calculation

Given the volume of the room is 225 m³ and the molar mass of air is 29 * 10^-3 kg/mol, we can calculate the number of air molecules in the room.

The number of moles of air in the room is given by: moles = volume / molar volume = 225 m³ / 29 * 10^-3 kg/mol = 7758.62 moles

Converting moles to molecules using Avogadro's number: number of molecules = moles * Avogadro's number number of molecules = 7758.62 moles * 6.022 x 10^23 molecules/mole = 4.67 x 10^27 molecules

Therefore, there are approximately 4.67 x 10^27 molecules of air in the room.

This calculation assumes ideal conditions and does not account for factors such as temperature and pressure variations within the room.