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30 ml of gas is changed from 4 atm to 2 atm what is the new volume

Sagot :

Sarah06109

Answer:

[tex]\boxed {\boxed {\sf 60 \ mL}}[/tex]

Explanation:

In this problem, volume and pressure are changing, so we use Boyle's Law. This states that the volume of a gas is inversely proportional to the pressure. The formula for this law is:

[tex]P_1V_1=P_2V_2[/tex]

Originally the gas has a volume of 30 milliliters and a pressure of 4 atmospheres.

[tex]4 \ atm * 30 \ mL=P_2V_2[/tex]

The pressure is changed to 2 atmospheres, but the new volume is unknown.

[tex]4 \ atm * 30 \ mL = 2 \ atm *V_2[/tex]

We want to solve for the new volume (Vā‚‚). It is being multiplied by 2 atmopsheres. The inverse operation of multiplication is division, so we divide both sides by 2 atm.

[tex]\frac{4 \ atm * 30 \ mL}{ 2 \ atm}= \frac{ 2 \ atm *V_2}{2 \ atm}[/tex]

[tex]\frac{4 \ atm * 30 \ mL}{ 2 \ atm}= V_2[/tex]

The units of atmospheres (atm) cancel.

[tex]\frac{4 * 30 \ mL}{ 2 }= V_2[/tex]

[tex]\frac{120 \ mL}{2}= V_2[/tex]

[tex]60 \ mL= V_2[/tex]

The new volume of the gas is 60 milliliters.

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