# Physics 212, Quiz #5a: Jan 14, 1998

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Helium gas contains molecules, each of which is a single helium atom. The mass of a helium atom is 4 atomic mass units.

Question 1: What is the mass of 1 mole of helium gas?

```  Answer: mass (grams) = mass of molecule (atomic mass units)

= 4 g

```

Joe places 2 grams of helium gas into a balloon.

Question 2: How many moles of helium are in the balloon?

```  Answer: # moles = (mass of sample)/(mass of 1 mole)

= (2 g)/(4 g) = 0.5 moles
```

Question 3: How many molecules of helium are in the balloon?

```  Answer: # molecules = (# of moles)*(Avagadro's number)

= (0.5) * (6.022 x 10^23) = 3.011 x 10^23

```

The balloon inflates to a diameter of 20 cm.

Question 4: What is the volume of the balloon, in cubic meters?

```  Answer:            4*pi
volume = ----- (radius)^3
3

4*pi*(0.10 m)^3
= --------------- = 4.19 x 10^(-3) m^3
3

```

The gas inside the balloon has a temperature of 25 degrees Celsius.

Question 5: What is the pressure of the gas inside the balloon?

```  Answer:  PV   =  nRT

Note that temperature must be expressed in Kelvin:

T(kelvin) = T(celsius) + 273 = 298 K

Solve for pressure P:

nRT     (0.5 moles)*(8.31 J/mol*K)*(298 K)
P = ------- = ----------------------------------
V             4.19 x 10^(-3) m^3

= 2.96 x 10^5 N/m^2 = 2.96 x 10^5 Pa

```