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A gas is in a closed container with a volume of 1 L and temperature of 300 K, giving it a pressure of 20 atm. Using the ideal gas law:

a) If the temperature is doubled and the volume remains the same, what is the new pressure in the container?
b) If the container is compressed to 0.5 L, what is the new pressure in the container? Assume the temperature does not change.
c) Explain why an aerosol can (e.g., hair spray, cooking spray) gets colder after you use it.

User Zac Kwan
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Final answer:

a) The new pressure is 166.20 atm. b) The new pressure is 332.40 atm. c) An aerosol can gets colder after you use it because of evaporative cooling.

Step-by-step explanation:

a) When the temperature is doubled and the volume remains the same, we can use the ideal gas law to find the new pressure. The ideal gas law equation is PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature in Kelvin.

To find the new pressure, we can rearrange the ideal gas law equation to solve for P:

P = (nRT) / V

Since the volume remains the same, we can simplify the equation to:

P = (nR) / V

When the temperature is doubled, we can plug in the new temperature value and the given values for volume and pressure:

Pnew = (nR) / V

Pnew = (nR) / V

Pnew = (20 * 8.31) / 1

Pnew = 166.20 atm

The new pressure in the container is 166.20 atm.

b) If the container is compressed to 0.5 L, we can use the ideal gas law to find the new pressure. The ideal gas law equation is PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature in Kelvin.

To find the new pressure, we can rearrange the ideal gas law equation to solve for P:

P = (nRT) / V

Since the pressure is constant, we can simplify the equation to:

P = (nR) / V

When the volume is changed to 0.5 L, we can plug in the new volume value and the given values for pressure and temperature:

Pnew = (nR) / Vnew

Pnew = (20 * 8.31) / 0.5

Pnew = 332.40 atm

The new pressure in the container is 332.40 atm.

c) An aerosol can gets colder after you use it because of the process known as evaporative cooling. When you spray the contents of the can, the liquid evaporates, turning into a gas. This process requires energy, which is taken from the surrounding environment, resulting in a decrease in temperature. As a result, the can feels cold when you use it.

User Mahmudur
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