30 cm3 of oxygen at 10 atmosphere pressure is placed in a 20 dm3 container. Calculate the new pressure if the temperature is kept constant.

30 cm3 of oxygen at 10 atmosphere pressure is placed in a 20 dm3 container. Calculate the new pressure if the temperature is kept constant.

Answer Details

Given:

• Initial pressure, 𝑃1=10P1​=10 atmospheres
• Initial volume, 𝑉1=30 cm3V1​=30cm3
• Final volume, 𝑉2=20 dm3V2​=20dm3

First, convert all volumes to the same units. Since 1 dm3dm3 is 1000 cm3cm3:

𝑉2=20 dm3=20×1000 cm3=20000 cm3V2​=20dm3=20×1000cm3=20000cm3

Now, using Boyle's Law:

𝑃1𝑉1=𝑃2𝑉2P1​V1​=P2​V2​

Substitute the known values into the equation:

10×30=𝑃2×2000010×30=P2​×20000

300=𝑃2×20000300=P2​×20000

Solve for 𝑃2P2​:

𝑃2=30020000P2​=20000300​

𝑃2=0.015 atmospheresP2​=0.015atmospheres

Therefore, the new pressure if the temperature is kept constant is: