Question

"A certain automobile tire has a volume of 0.0185 m3. If the absolute (or total) pressure in the tire is 500 kPa and the temperature is 298 K, how many molecules are there inside the tire? (R = 8.31 J/mol • K, NA = 6.022 x 1023 molecules/mol)"

Answer 1

The answer to your question is 2.24 x 1024 molecules

Step-by-step explanation:

Data

Volume = 0.0185 m³

Pressure = 500 kPa

Temperature = 298°K

number of molecules = ?

R = 8.31 J/molK

NA = 6.022 x 10²³

Process

1.- Write the equation of ideal gases and solve for "n"

PV = nRT

n = (PV) / (RT)

2.- Substitute to find "n"

n = (500000 x 0.0185 ) / (8.31 x 298)

Simplify

n = 9250 / 2476.4

result

n = 3.73 moles

3.- Calculate the number of molecules

1 mol ------------------------ 6.022 x 10²³ molecules

3.73 moles ----------------- x

x = (3.73 x 6.022 x 10²³) / 1

x = 2.24 x 1024 molecules