Question

Find P2 if a gas changes from 25 oC and 87 kPa to 50 oC.

Answer 1

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:
`\displaystyle (P_1)/(T_1) = (P_2)/(T_2)`

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

Step-by-step 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]:
   `\displaystyle (87 \ kPa)/(323.15 \ K) = (P_2)/(298.15 \ K)`
2. Cross-multiply:
   `\displaystyle 25939.1 \ kPa \cdot K = (323.15 \ K)P_2`
3. Isolate P₂:
   `\displaystyle \80.2694 \ kPa = P_2`
4. Rewrite:
   `\displaystyle P_2 = 80.2694 \ kPa`

Step 5: Check

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

80.2694 kPa ≈ 80 kPa