A gaseous air~fuel mixture in a sealed car engine cylinder has an initial volume of GOD. ml. at 1. atm. To prepare for ignition of the fuel, a piston moves within the cylinder, reducing the volume of the air-fuel mixture to 50.mL at constant temperature. Assuming ideal behavior, what is the new pressure of the airvfuel mixture?

A. About 0.083 atm, because the initial volume of the gas mixture was 12 times larger than its final volume.

B. About 12 atm, because the volume of the gas mixture decreased by a factor of 12.

C.. About 120. atm, because the initial volume of the gas mixture was 120 times larger than its final volume.

D.. About 550. atm, because the change in the volume of the gas mixture was 550. mL.

 

Answer:

B. About 12.0 atm because the volume of the gas mixture decreased by a factor of 12

Step-by-step explanation

Boyle's Law states that within a closed system and at a constant temperature the pressure of the gas is inversely proportional to its volume. If the volume of the gaseous air-fuel mixture is reduced at a constant temperature, the pressure of the gaseous air-fuel mixture is increased.

To calculate the new pressure of the gaseous air-fuel mixture, we can use Boyle's Law.

This can be stated mathematically as follows:

P₁V₁=P₂V₂

Where P₁ =1.0 atm

V₁ = 600.0 mL

V₂ = 50.0 mL

P₂= new pressure of the gas

Rearrange the equation

P₂ = P₁V₁/V₂

P₂ = (1.0 atm *600.0mL)/ (50.0 mL)

P₂ = 12.0 atm

We can also calculate the new pressure of the gaseous air-fuel mixture, by calculating the ratio of volume.

V₁ /V₂= 600.0 mL/ 50.0 mL =12

We know, P*V = constant.

P₂ = 12.0 *1.0 atm =12.0 atm

The volume of the gaseous air-fuel mixture decreased by a factor 12, thus the pressure of the gaseous air-fuel mixture will be increased by a factor 12.

Therefore, the correct option is B. About 12.0 atm because the volume of the gas mixture decreased by a factor of 12