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Problem : 3.0 moles of gas at 300 K and 1.0 atm have a volume of 15 smoots. What is R in ?

Rearrange PV = nRT to solve for R: = R. Plug in the values of P, V, n, and T to solve for R. R = 0.017 .

Problem : A sample of gas at 1.0 atm and 298 K has a volume of 8.7 L. How much gas does the sample contain?

Rearrange PV = nRT to solve for n. = n. Let's try converting everything to SI units so that we can used the gas constant value of 8.314 . 1.0 atm converts to 1.0×105 Pa. There are 10-3 m3 in a liter, so 8.7 L converts to 8.7×10-3 m3. Plugging in these values, we find that n = 0.35 mol.

Problem : You are the head engineer at a chemical plant. Sam Yagan, the summer intern, has just broken the cooling system to the main helium tank. Sam tells you not to be worried; the tank can withstand up to 40.0 atm of pressure before exploding. Before Sam's accident, the tank was subjected to 10.0 atm. The tank was originally at 250 K, but it's a hot summer day, and you fear its temperature may rise to 350 K. Should you believe Sam?

The key to this problem is to realize which values are constant. V, n, and R do not change. P and T do. Rearrange PV = nRT so that the variables and constants are on opposite sides of the "=" sign:

= = C    

Since the C is constant regardless of P and T, we can rearrange the equation in to a more useful form:

=    

Plug in the given values for P and T. The pressure in the tank will only rise to 14 atm. Sam is correct; there is no immediate danger from the rise in temperature. That coolant system must have had a purpose, though, and you should repair it ASAP.

Problem : A race of purely gas-based aliens inhabits Jupiter (P = 808 kPa, T = 600 K). On Jupiter, each alien occupies a volume of one cubic meter. The aliens decide to visit Earth. They board their climate controlled gascraft, make the long journey to Earth, and land in a cornfield in southern Idaho (P = 101 kPa, T = 300 K ). When they disembark, how big will they be? Assume that the aliens' innards do not diffuse or burst in the Earth's atmosphere.

P, T, and V are the variables in this problem. n is constant. Place the constants and variables on opposite sides of the "=" sign:

= n    

We can rearrange this equation:

= →V2 =    

Solving for V2, we find that the aliens will have a volume of four cubic meters.
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