How many moles are there in a 30 cm diameter basketball at a pressure of 160 kpa and temperature of 25 degree celcius.
calculate volume.
PV=nRT find n
To determine the number of moles in a basketball, we need to use the Ideal Gas Law equation:
PV = nRT,
where:
P = pressure (in Pascals),
V = volume (in cubic meters),
n = number of moles,
R = ideal gas constant (8.314 J/(mol·K)),
T = temperature (in Kelvin).
To answer your question, we first need to convert the given information to the appropriate units:
Given:
Pressure (P) = 160 kPa
Temperature (T) = 25 degrees Celsius
Diameter (D) = 30 cm
Step 1: Convert the pressure to the appropriate unit (Pascals):
1 kPa = 1000 Pa
Therefore, 160 kPa = 160,000 Pa.
Step 2: Convert the temperature to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 25 + 273.15
T(K) = 298.15 K.
Step 3: Calculate the volume of the basketball:
The volume of a sphere is given by the formula: V = (4/3) * π * r^3
In this case, we need to use the diameter (D) to find the radius (r) of the basketball:
Radius (r) = D/2
r = 30 cm / 2
r = 15 cm
Now, we have the radius (r), so we can calculate the volume (V):
V = (4/3) * π * (15 cm)^3
For accuracy, we'll convert cm^3 to m^3 (since the ideal gas constant (R) is in SI units):
1 m^3 = 1,000,000 cm^3
V(m^3) = V(cm^3) / 1,000,000
Step 4: Substitute the given values into the Ideal Gas Law equation, PV = nRT:
n = (PV) / (RT)
Now, substitute the known values:
P = 160,000 Pa
V(m^3) = V(cm^3) / 1,000,000
R = 8.314 J/(mol·K)
T = 298.15 K
n = (160,000 Pa * V(cm^3) / 1,000,000) / (8.314 J/(mol·K) * 298.15 K)
After calculating the volume and rearranging the equation to solve for n, you'll have the number of moles in the basketball.