A weather balloon is inflated with helium to a volume of 28.1 L at a pressure of 754 torr and a temperature of 26.0 Celsius. The balloon rises in the atmosphere to an altitude where the pressure is 380 torr and the temperature is -16.1 degree Celsius.

1. Calculate the number of helium atoms per liter for both altitudes.

Is it 2.44 x 10^22 He atoms per liter?

2. Calculate the gas density (g/mL) for each altitude (AW He= 4.00 g/mol).

1 no.

PV = nRT and solve for n = number of mols. Then n x 6.022E23 = number He atoms. Same at both temperatures.

2. density = P*molar mass/RT gives density in g/L. Convert to g/L.

To calculate the number of helium atoms per liter at each altitude, we can use the ideal gas law equation, which states:

PV = nRT

Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = gas constant (0.0821 L•atm/(mol•K))
T = temperature (in Kelvin)

Step 1: Convert the given temperature and pressures to Kelvin and atm.

Temperature at the first altitude = 26.0 Celsius = 26.0 + 273.15 = 299.15 K
Temperature at the second altitude = -16.1 Celsius = -16.1 + 273.15 = 257.05 K

Pressure at the first altitude = 754 torr = 754/760 atm (approximately) = 0.991 atm
Pressure at the second altitude = 380 torr = 380/760 atm (approximately) = 0.500 atm

Step 2: Calculate the number of moles at both altitudes using the ideal gas law.

For the first altitude:
n1 = (P1 * V1) / (R * T1)
= (0.991 atm * 28.1 L) / (0.0821 L•atm/(mol•K) * 299.15 K)
≈ 1.157 moles

For the second altitude:
n2 = (P2 * V2) / (R * T2)
= (0.500 atm * 28.1 L) / (0.0821 L•atm/(mol•K) * 257.05 K)
≈ 0.718 moles

Step 3: Calculate the number of helium atoms per liter at both altitudes.

To calculate the number of helium atoms, we multiply the number of moles by Avogadro's constant (6.022 x 10^23 atoms/mol) and divide by the volume.

For the first altitude:
Number of helium atoms per liter at the first altitude = (1.157 moles * 6.022 x 10^23 atoms/mol) / 28.1 L
≈ 2.482 x 10^22 He atoms per liter

For the second altitude:
Number of helium atoms per liter at the second altitude = (0.718 moles * 6.022 x 10^23 atoms/mol) / 28.1 L
≈ 1.537 x 10^22 He atoms per liter

Therefore, the number of helium atoms per liter for the first altitude is approximately 2.482 x 10^22 He atoms per liter, and for the second altitude is approximately 1.537 x 10^22 He atoms per liter.

Moving on to the second question:

To calculate the gas density (g/mL) at each altitude, we need to find the mass of helium gas present in one liter of volume.

Step 1: Calculate the mass of helium gas using the moles of helium at each altitude.

For the first altitude:
Mass of helium at the first altitude = n1 * Molar mass of helium
= 1.157 moles * 4.00 g/mol
= 4.628 g

For the second altitude:
Mass of helium at the second altitude = n2 * Molar mass of helium
= 0.718 moles * 4.00 g/mol
= 2.872 g

Step 2: Calculate the gas density at each altitude by dividing the mass of helium by the volume in milliliters.

For the first altitude:
Gas density at the first altitude = Mass of helium at the first altitude / Volume at the first altitude
= 4.628 g / 28.1 L
≈ 0.165 g/L

For the second altitude:
Gas density at the second altitude = Mass of helium at the second altitude / Volume at the second altitude
= 2.872 g / 28.1 L
≈ 0.102 g/L

Therefore, the gas density at the first altitude is approximately 0.165 g/mL, and at the second altitude is approximately 0.102 g/mL.