Respuesta :

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Answer:

P₂ ≈ 80 kPa

General Formulas and Concepts:

Math

Pre-Algebra

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Algebra I

  • Equality Properties

Chemistry

Unit 0

Temperature Conversion: K = °C + 273.15

Gas Laws

Gay-Lussac's Law: [tex]\displaystyle \frac{P_1}{T_1} = \frac{P_2}{T_2}[/tex]

  • P is pressure
  • T is temperature (in Kelvins)

Explanation:

Step 1: Define

P₁ = 87 kPa

T₁ = 50 °C

T₂ = 25 °C

P₂ = ?

Step 2: Identify Conversions

Kelvin Temp Conversion

Step 3: Convert

T₁ - 50 °C + 273.15 = 323.15 K

T₂ - 25 °C + 273.15 = 298.15 K

Step 4: Solve for P₂

  1. Substitute [GLL]:                    [tex]\displaystyle \frac{87 \ kPa}{323.15 \ K} = \frac{P_2}{298.15 \ K}[/tex]
  2. Cross-multiply:                      [tex]\displaystyle 25939.1 \ kPa \cdot K = (323.15 \ K)P_2[/tex]
  3. Isolate P₂:                              [tex]\displaystyle \80.2694 \ kPa = P_2[/tex]
  4. Rewrite:                                 [tex]\displaystyle P_2 = 80.2694 \ kPa[/tex]

Step 5: Check

We are given 1 sig fig as our lowest. Follow sig fig rules and round.

80.2694 kPa ≈ 80 kPa

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