Answer to Question #179101 in Chemistry for moon

Question

Solve the following problem

1. A gas occupies a volume of 500 cm 3 at 27⁰C. What will be the volume of the gas when

the temperature is -48⁰C? Assume pressure and moles are constant.

2. The pressure in an automobile tire is 29.8 psi on a cold morning of 20°C. After it is

driven a while, the temperature rises to 43°C. What is the pressure in the tire assuming

that the volume remains constant?

Answer 1

Solution:

Question 1:

T₁ = 27°C + 273 = 300 K

V₁ = 500 cm³

T₂ = -48°C + 273 = 225 K

V₂ = unknown

P₁ = P₂ = const

n₁ = n₂ = const

Since the pressure and amount of gas remain unchanged, Charles' Law can be used.

Charles' Law can be expressed as: V₁ / T₁ = V₂ / T₂

V₁T₂ = V₂T₁

To find the volume, solve the equation for V₂:

V₂ = V₁T₂ / T₁

V₂ = (500 cm³ × 225 K) / (300 K) = 375 cm³

V₂ = 375 cm³

 

Answer to Question 1: The volume of the gas will be 375 cm³.

Question 2:

P₁ = 29.8 psi 

T₁ = 20°C + 273 = 293 K

P₂ = unknown

T₂ = 43°C + 273 = 316 K

V₁ = V₂ = const

n₁ = n₂ = const

Since the volume and amount of gas remain unchanged, Gay-Lussac's Law can be used.

Gay-Lussac's Law can be expressed as: P₁ / T₁ = P₂ / T₂

P₁T₂ = P₂T₁

To find the pressure, solve the equation for P₂:

P₂ = P₁T₂ / T₁

P₂ = (29.8 psi × 316 K) / (293 K) = 32.14 psi

P₂ = 32.14 psi

Answer to Question 2: The pressure in the tire will be 32.14 psi.