Question

A sample of nitrogen is initially at a pressure of 1.7 kPa, a temperature of -10 C and a volume of 7.5 m3. Then the volume is decreased to 3.8 m3. the temperature is decreased to 200 K. What is the final pressure of the nitrogen gas?

Answer 1

`\boxed{\text{2.6 kPa}}`

Step-by-step explanation:

To solve this problem, we can use the Combined Gas Laws:

`(p_(1)V_(1) )/(T_(1)) = (p_(2)V_(2) )/(T_(2))`

Data:

p₁ = 1.7 kPa; V₁ = 7.5 m³; T₁ = -10 °C

p₂ = ?; V₂ = 3.8 m³; T₂ = 200 K

Calculations:

(a) Convert temperature to kelvins

T₁ = (-10 + 273.15) K = 263.15 K

(b) Calculate the pressure

`\begin{array}{rcl}(1.7 * 7.5 )/(263.15) & = & (p_(2) * 3.8)/(200)\\\\0.0485 & = & 0.0190p_(2)\\p_(2) & = & \textbf{2.6 kPa}\\\end{array}\\\text{The new pressure of the gas is \boxed{\textbf{2.6 kPa}}}`