Question

Яка кількість речовини міститься в 3 м 3 газу, якщо тиск дорівнює 300 кПа, а температура 27 °С ? (задача)

Answer 1

Ответ:

Объяснение:

Дано:

V = 3 м³

p = 300 кПа = 3 * 10⁵ Па

Т = 27°C = 300 K

Найти: ν - ?

З рівняння Клапейрона-Менделєєва:

pV = νRT  =>  ν = pV / (RT)

ν = 3 * 10⁵ * 3 / (8,31 * 300) = 361 моль

Answer 2

Calculation of the Amount of Substance in a Gas

To calculate the amount of substance in a gas, we can use the ideal gas law equation, which states:

PV = nRT

Where: - P is the pressure of the gas (in pascals) - V is the volume of the gas (in cubic meters) - n is the amount of substance (in moles) - R is the ideal gas constant (8.314 J/(mol·K)) - T is the temperature of the gas (in Kelvin)

In this case, we are given: - P = 300 kPa (300,000 pascals) - V = 3 m^3 (cubic meters) - T = 27 °C (27 degrees Celsius)

To solve for n, we need to convert the given values to the appropriate units.

Conversion of Units

First, let's convert the pressure from kilopascals to pascals: - 1 kPa = 1000 Pa - Therefore, 300 kPa = 300,000 Pa

Next, let's convert the temperature from Celsius to Kelvin: - To convert from Celsius to Kelvin, we add 273.15 to the Celsius value. - Therefore, 27 °C = 27 + 273.15 = 300.15 K

Now, we have the following values: - P = 300,000 Pa - V = 3 m^3 - T = 300.15 K

Calculation

Substituting the values into the ideal gas law equation, we have:

PV = nRT

(300,000 Pa) * (3 m^3) = n * (8.314 J/(mol·K)) * (300.15 K)

Simplifying the equation, we can solve for n:

n = (300,000 Pa * 3 m^3) / (8.314 J/(mol·K) * 300.15 K)

n ≈ 361.48 moles

Therefore, the amount of substance in the gas is approximately 361.48 moles.

Summary

In summary, if the pressure of the gas is 300 kPa and the temperature is 27 °C, with a volume of 3 m^3, the amount of substance in the gas is approximately 361.48 moles.