Question

A 1.2 μL ampoule of xenon has a pressure

of 3 Torr at 22°C. How many Xe atoms are
present?
Answer in units of atoms.

Answer 1

ANSWER -

To calculate the number of xenon atoms present in the ampoule, we can use the ideal gas law:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature.

First, we need to convert the volume of the ampoule to liters:

1.2 μL = 1.2 × 10^-6 L

Next, we can plug in the given values and solve for the number of moles of xenon:

n = PV/RT

where:

P = 3 Torr = 0.003947 atm (since 1 Torr = 1/760 atm)
V = 1.2 × 10^-6 L
R = 0.08206 L·atm/(mol·K)
T = 22 + 273 = 295 K

Plugging in these values, we get:

n = (0.003947 atm) * (1.2 × 10^-6 L) / (0.08206 L·atm/(mol·K) * 295 K)

n = 2.37 × 10^-11 mol

Finally, we can use Avogadro's number to convert from moles to atoms:

number of atoms = n * N_A

where N_A is Avogadro's number (6.022 × 10^23 atoms/mol).

Plugging in the values, we get:

number of atoms = 2.37 × 10^-11 mol * 6.022 × 10^23 atoms/mol

number of atoms = 1.43 × 10^13 atoms

Therefore, there are approximately 1.43 × 10^13 xenon atoms present in the ampoule.

Answer 2

Approximately 3.81×10^13 xenon atoms are present in the 1.2 μL ampoule.

Step-by-step explanation:

To find the number of xenon atoms present in the 1.2 μL ampoule, we can use the ideal gas law, which relates the number of gas particles to the pressure, volume, and temperature of the gas:

PV = nRT

where P is the pressure, V is the volume, n is the number of particles (in moles), R is the gas constant, and T is the temperature.

We need to first calculate the number of moles of xenon present in the ampoule:

n = PV/RT

where P is in atm, V is in liters, R = 0.08206 L·atm/(mol·K) is the gas constant, and T is in kelvin.

Converting the given pressure of 3 Torr to atm and the volume of 1.2 μL to liters:

P = 3 Torr = 3/760 atm

V = 1.2 μL = 1.2×10^-6 L

Substituting these values, along with the temperature of 22°C = 295 K:

n = (3/760) atm × (1.2×10^-6 L) / (0.08206 L·atm/(mol·K) × 295 K)

n = 6.33×10^-11 mol

Finally, we can use Avogadro's number, which gives the number of particles in one mole of a substance:

1 mol Xe = 6.022×10^23 Xe atoms

Multiplying the number of moles by Avogadro's number, we get:

6.33×10^-11 mol Xe × (6.022×10^23 Xe atoms/mol) = 3.81×10^13 Xe atoms

Therefore, there are approximately 3.81×10^13 xenon atoms present in the 1.2 μL ampoule.