An automobile tire has a volume of 0.0185 m3. If the pressure in the tire is 500 kPa and the temperature is 298 K, how many molecules are there inside the tire?
2.25*10^24
To calculate the number of molecules inside the tire, we first need to determine the number of moles of gas using the ideal gas law.
Step 1: Convert the pressure from kPa to Pa.
1 kPa = 1000 Pa
So, the pressure is 500 kPa * 1000 = 500,000 Pa.
Step 2: Convert the volume from m^3 to liters.
1 m^3 = 1000 liters
So, the volume is 0.0185 m^3 * 1000 = 18.5 liters.
Step 3: Convert the temperature from Kelvin to Celsius.
The temperature in Celsius is 298 K - 273.15 = 24.85 °C.
Step 4: Convert the volume from liters to m^3.
1 liter = 0.001 m^3
So, the volume is 18.5 liters * 0.001 = 0.0185 m^3.
Step 5: Calculate the number of moles using the ideal gas law.
PV = nRT,
where P is the pressure in Pa, V is the volume in m^3, n is the number of moles, R is the ideal gas constant (8.314 J/(mol·K)), and T is the temperature in Kelvin.
n = PV / RT
= (500,000 Pa) * (0.0185 m^3) / (8.314 J/(mol·K) * 298 K)
= 92425 / 2469.79172
≈ 37.41 moles.
Step 6: Calculate the number of molecules using Avogadro's number.
1 mole = 6.022 x 10^23 molecules
So, the number of molecules is 37.41 moles * (6.022 x 10^23 molecules/mole)
= 2.250 x 10^25 molecules.
Therefore, there are approximately 2.250 x 10^25 molecules inside the tire.
To determine the number of molecules inside the tire, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure (in pascals)
V is the volume (in cubic meters)
n is the number of moles
R is the gas constant (8.314 J/(mol·K))
T is the temperature (in Kelvin)
First, we need to convert the pressure from kPa to pascals:
500 kPa = 500,000 Pa
Next, we can calculate the number of moles using the ideal gas law equation:
n = PV / RT
Let's plug in the values:
n = (500,000 Pa) * (0.0185 m3) / ((8.314 J/(mol·K)) * (298 K))
Now, let's simplify the equation:
n = (500,000 Pa * 0.0185 m3) / (8.314 J/(mol·K) * 298 K)
Calculating further:
n ≈ 35.84 moles
Finally, to find the number of molecules, we use Avogadro's number (6.022 x 10^23 molecules/mol):
Number of molecules = n * Avogadro's number
Number of molecules ≈ (35.84 moles) * (6.022 x 10^23 molecules/mol)
Calculating further, we get:
Number of molecules ≈ 2.16 x 10^25 molecules
Therefore, there are approximately 2.16 x 10^25 molecules inside the tire.
PV=nRT solve for number of moles, n
then multiply by avag number.