A spherical balloon of 21 cm diameter is to be filled up with hydrogen at NTP from a cylinder containing the gas at 20 atmospheres at 27°C. If the cylinder can hold 2.82 L of water, calculate the number of balloons that can be filled up.Correct answer is '10'. Can you explain this answer?

Question

A spherical balloon of 21 cm diameter is to be filled up with hydrogen at NTP from a cylinder containing the gas at 20 atmospheres at 27&deg;C. If the cylinder can hold 2.82 L of water, calculate the number of balloons that can be filled up.Correct answer is '10'. Can you explain this answer?

Answer

To solve this problem, we can use the ideal gas law equation, which states:

PV = nRT

Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature

First, let's convert the diameter of the balloon to radius:
radius = diameter / 2
radius = 21 cm / 2 = 10.5 cm = 0.105 m

Next, let's find the volume of the balloon:
volume = (4/3) * π * (radius^3)
volume = (4/3) * 3.14159 * (0.105^3)
volume ≈ 0.000521 m^3

Now, let's convert the pressure from atmospheres to Pascals:
pressure = 20 atmospheres * 101325 Pa/atmosphere
pressure ≈ 2,026,500 Pa

Next, let's convert the temperature from degrees Celsius to Kelvin:
temperature = 27°C + 273.15 K/°C
temperature ≈ 300.15 K

Now, we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = (PV) / (RT)
n = (2,026,500 Pa * 0.000521 m^3) / ((0.08206 L * atm / K * mol) * 300.15 K)
n ≈ 0.041 moles

Therefore, the number of moles of hydrogen required to fill the balloon is approximately 0.041 moles.

Answer

To solve this problem, we can use the ideal gas law, which states:

PV = nRT

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

First, let's convert the diameter of the balloon to radius:

Radius = Diameter / 2 = 21 cm / 2 = 10.5 cm = 0.105 m

The volume of the balloon can be calculated using the formula for the volume of a sphere:

V = (4/3)πr^3

V = (4/3)π(0.105 m)^3
V = 0.000515 m^3

Next, we need to convert the pressure from 20 atmospheres to Pascals:

1 atm = 101325 Pa
20 atm = 20 * 101325 Pa = 2026500 Pa

Now, let's convert the temperature from degrees Celsius to Kelvin:

NTP (Normal Temperature and Pressure) is defined as 0 degrees Celsius or 273 Kelvin.

Now we can use the ideal gas law to find the number of moles of hydrogen:

PV = nRT

n = PV / RT

n = (2026500 Pa) * (0.000515 m^3) / ((0.0821 L·atm/(mol·K)) * 273 K)

n = 0.0407 moles

Therefore, the spherical balloon can be filled with approximately 0.0407 moles of hydrogen at NTP from the given cylinder.

Similar Chemistry Doubts

A spherical balloon of 21 cm diameter is to be filled up with hydrogen at NTP from a cylinder containing the gas at 20 atmospheres at 27C. If the cylinder can hold 2.82 L of water, calculate the number of balloons that can be filled up. Correct answer is '48.5'. Can you explain this answer?

The vapor density of a mixture containing NO2 and N2O4 is 38.3 at 26.70C. Calculate no of moles of NO2 in 100g mixture: [up to three decimal places] Correct answer is between '0.430,0.440'. Can you explain this answer?

Calculate the radius (Å) of one molecule of water [Assuming it as spherical and having density 1g/mL]. (rounded up to onedecimal plac e) Correct answer is between '1.8,2.0'. Can you explain this answer?

An aqueous solution containing 288 g of a nonvolatile compound having the stoichiometric composit ion CxH2xOx in 90 g water boils at 101.24C at 1 atmospheric pressure. What is the value of x? (Given that: Kb(H2O) = 0.512 K Kg mol1): Correct answer is '44'. Can you explain this answer?

Top Courses for Chemistry

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams