A 6.00 ft cylinder has a radius of 26 in. It contains 189 lb of helium at 25 celsius. Express the volume of the cylinder (V=ðr²h) in liters, the amount of helium in moles and the temperature in Kelvin.
Convert 6 ft to cm, 26 inches to cm and 189 lb to grams.
V = pi*h*r^2
Kelvin = 273 + C.
mols = grams/molar mass
To express the volume of the cylinder in liters, we need to convert both the radius and the height to centimeters. Since 1 foot is equal to 12 inches and 1 inch is equal to 2.54 centimeters, the height of the cylinder can be converted as follows:
Height = 6.00 ft * 12 in/ft * 2.54 cm/in = 182.88 cm
Now, we can calculate the volume using the formula V = πr²h, where π is approximately 3.14159:
Volume = 3.14159 * (26 in/2.54 cm)² * 182.88 cm = 379,766.14 cm³
To convert the volume from cm³ to liters, divide by 1000:
Volume = 379,766.14 cm³ / 1000 = 379.76614 liters
Therefore, the volume of the cylinder is approximately 379.76614 liters.
To calculate the amount of helium in moles, we need to use the ideal gas law:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, we need to convert the pressure from lb/in² to atm. Since 1 atm is equal to 14.696 lb/in²:
Pressure = 189 lb/in² / 14.696 lb/in²/atm ≈ 12.8603 atm
Next, we need to convert the temperature from Celsius to Kelvin. To do this, we add 273.15 to the Celsius temperature:
Temperature = 25 °C + 273.15 = 298.15 K
Now, we can rearrange the ideal gas law to solve for the number of moles:
n = PV / RT
Substituting the values:
n = 12.8603 atm * 379.76614 liters / (0.0821 L·atm/mol·K * 298.15 K) ≈ 177.6989 mol
Therefore, the amount of helium in the cylinder is approximately 177.6989 moles.
Finally, the temperature in Kelvin is already calculated as 298.15 K in the previous step.
To start, let's convert the measurements to a consistent unit system. We'll convert feet to inches and pounds to grams.
1. Converting the height of the cylinder from feet to inches:
6.00 ft * 12 in/ft = 72.00 in
2. Converting the radius of the cylinder from inches to centimeters:
26 in * 2.54 cm/in = 66.04 cm
3. Converting the volume of the cylinder from cubic inches to liters:
V = π * r² * h
V = π * (66.04 cm)² * (72.00 in * 2.54 cm/in)
V = π * (66.04 cm)² * (182.88 cm)
V = π * 27016.6416 cm³
V ≈ 84962.33 cm³
Since 1 cm³ = 1 mL and 1 L = 1000 mL, we have:
V ≈ 84962.33 mL = 84.96233 L
Therefore, the volume of the cylinder is approximately 84.96233 liters.
4. Converting the mass of helium from pounds to grams:
189 lb * 453.59237 g/lb = 85549.20493 g
5. Converting the temperature from Celsius to Kelvin:
Kelvin = Celsius + 273.15
T(K) = 25 °C + 273.15 = 298.15 K
6. Calculating the amount of helium in moles using the ideal gas law:
PV = nRT
We first need to find the pressure (P). If it's not provided, we can assume atmospheric pressure, which is around 1 atm.
R is the ideal gas constant, which is approximately 0.0821 L·atm/mol·K.
Rearranging the formula, we get:
n = PV / RT
n = (1 atm * 84.96233 L) / (0.0821 L·atm/mol·K * 298.15 K)
n ≈ 3.5304 moles
Therefore, the amount of helium in the cylinder is approximately 3.5304 moles, to three decimal places.
So, the volume of the cylinder is approximately 84.96233 liters, the amount of helium is approximately 3.5304 moles, and the temperature is approximately 298.15 Kelvin.