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For many purposes we can treat methane (CH) as an ideal gas at temperatures above its boiling point of -161. °C. Suppose the temperature of a sample of methane gas is raised from -13.0 °C to 17.0°C, and at the same time the pressure is changed. If the initial pressure was 0.26 kPa and the volume increased by 30.0%, what is the final pressure? Round your answer to the correct number of significant digits.

Answer :

Edufirst

Answer:

  • 0.26kPa

Explanation:

You can use the combined gas law:

         

         [tex]\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}[/tex]

You need to find P₂ when:

  • T₁ = - 13.0 + 273.15  K = 260.15 K
  • T₂ = 17.0 + 273.15 K = 290.15 K
  • P₁ = 0.26 kPa
  • V₂ = 1.300·V₁

Thus, clear P₂ from the equation, subsitute and compute:

        [tex]P_2=\dfrac{P_1V_1T_2}{V_2T_1}[/tex]

        [tex]P_2=\dfrac{0.26kPa\cdot V_1\cdot 290.15K}{1.300V_1\cdot 260.15K}[/tex]

       

         P₂ = 0.26kPa ← answer

Since the factor P₁ has two significant figures, the result is limited to two significant figures.

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