The Goodyear blimps, which frequently fly over sporting events, hold approximately 1.90×10^5 ft^3 of helium. If the gas is at 25 C and 1.0 atm, what mass of helium is in the blimp?

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To find the mass of helium in the blimp, we can use the ideal gas law equation:

PV = nRT

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

First, let's convert the given volume of the blimp from cubic feet to liters:

1 ft^3 = 28.3168 L

So, the volume of the blimp in liters is:

V = 1.90 × 10^5 ft^3 × 28.3168 L/ft^3
V ≈ 5.38 × 10^6 L

Next, let's convert the given temperature from Celsius to Kelvin:

T(K) = T(°C) + 273.15
T(K) = 25°C + 273.15
T(K) ≈ 298.15 K

Now, we can substitute the given values into the ideal gas law equation:

PV = nRT

(1.0 atm) × (5.38 × 10^6 L) = n × (0.0821 L.atm/mol.K) × (298.15 K)

Simplifying:

5.38 × 10^6 L.atm = 24.738 × n

Dividing both sides by 24.738:

n ≈ 5.38 × 10^6 L.atm / 24.738

n ≈ 217843.4478 mol

Finally, we can calculate the mass of helium using the molar mass of helium:

Molar mass of helium (He) = 4.0026 g/mol

Mass = n × molar mass
Mass ≈ (217843.4478 mol) × (4.0026 g/mol)

Mass ≈ 871468.25 g

Therefore, the mass of helium in the blimp is approximately 871,468.25 grams.

To calculate the mass of helium in the blimp, we need to use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.

First, let's convert the given temperature of 25°C to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 25 + 273.15
T(K) = 298.15 K

Next, let's convert the given volume of the blimp from ft^3 to cubic meters (m^3):
1 ft^3 = 0.02832 m^3
1.90×10^5 ft^3 = 1.90×10^5 × 0.02832 m^3
Volume (V) = 5380.8 m^3

Now, we can rearrange the ideal gas law equation to solve for the number of moles of gas (n):
n = PV / RT

We know the pressure (P) is 1.0 atm and the ideal gas constant (R) is 0.0821 L·atm/(mol·K). Let's convert the volume (V) from cubic meters (m^3) to liters (L):
1 m^3 = 1000 L
5380.8 m^3 = 5380.8 × 1000 L
Volume (V) = 5.3808×10^6 L

Now we can calculate the number of moles (n):
n = (1.0 atm) × (5.3808×10^6 L) / ((0.0821 L·atm/(mol·K)) × (298.15 K))

Simplifying the equation:
n = 1.0 × 5.3808×10^6 / (0.0821 × 298.15)

Finally, we can calculate the mass (m) of helium:
m = n × M
where M is the molar mass of helium, which is 4.0026 g/mol.

Now, we can substitute the value of n into the equation to find the mass of helium in grams:
m = (1.0 × 5.3808×10^6 / (0.0821 × 298.15)) × 4.0026

Calculating the value of m will give us the final answer for the mass of helium in the blimp.

Convert 1.9 x 10^5 ft^3 to liters, use PV = nRT to solve for n, number of moles, and obtain grams from that. Then convert back to cubic feet is that is the desired unit.