Respuesta :

Answer:

2.83 kg

Explanation:

Given:

Volume, V = 0.8 m³

gage pressure, P = 200 kPa

Absolute pressure = gage pressure + Atmospheric pressure

= 200 + 101 = 301 kPa = 301 × 10³ N/m²

Temperature, T = 23° C = 23 + 273 = 296 K

Now,

From the ideal gas equation

PV = mRT

Where,

m is the mass

R is the ideal gas constant = 287 J/Kg K. (for air)

thus,

301 × 10³ × 0.8 = m × 287 × 296

or

m = 2.83 kg

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The mass of the air in the tire is 1040.192 grams.

We must know the concept of the Ideal Gas Equation to solve this question.

What is Ideal Gas Equation?

The Ideal Gas Equation shows the empirical relationship between the Volume, Pressure, Temperature, and the number of moles in a given substance.

Using Ideal Gas Equation:

PV = nRT

From the given information:

  • The volume of the air O₂ = 0.8 m³ = 0.8 × 1000 L = 800 L
  • The pressure = 200 KPa
  • The temperature = 23°C = (273 + 23) K = 296 K
  • The rate constant = 8.31446 L.kPa.K⁻¹.mol⁻¹

[tex]\mathbf{200 kPa \times 800 \ L = n \times 8.31446 L.kPa.K^{-1}.mol^{-1} \times 296 \ K }[/tex]

[tex]\mathbf{n = \dfrac{200 kPa \times 800 \ L}{8.31446 \ L.kPa.K^{-1}.mol^{-1} \times 296 \ K}}[/tex]

[tex]\mathbf{n =65.012 \ mol}[/tex]

From the relation;
Number of moles = mass/molar mass.

  • The molar mass of O₂ = 16 g/mol

Mass of air (O₂) = number of moles × molar mass

Mass of air (O₂) = 65.012 mol × 16 g/mol

Mass of air (O₂) = 1040.192 grams

Learn more about ideal gas equation here:

https://brainly.com/question/25290815

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