Respuesta :
Answer:
3.39
Explanation:
Given that
Volume, v = 3.92*10^3 cm³ we convert the volume from cm³ to m³ and we have 0.00392
Pressure, P = 1.25*10^5 Pa
Average Kinetic Energy, K.E = 3.6*10^-22 J
We use the gas law formula,
PV = nRT
Making n subject of the formula, we have
n = PV/RT
Solving for n, we have
n = (1.25*10^5 Pa * 0.00392 m³) / 8.314 * T
n = 4.9*10^8 / 8.314 * T
n = 490 / 8.314T
n = 58.94/T
Note that average kinetic energy is given as
K.E(avg) = 3/2K.T,
3/2 K.T = 3.6*10^-22 J
where K = 1.38*10^-23
T = (3.6*10^-22 J * 2) / (3 * 1.38*10^-23)
T = 17.39
Substitute for T, we have
n = 58.94 / 17.39
n = 3.39
The number of moles of helium that are in the spherical balloon is equal to 3.39 moles.
Given the following data:
- Volume = [tex]3.92 \times 10^3\;cm^3[/tex] to [tex]m^3 = 3.92 \times 10^{-3}\;m^3[/tex]
- Pressure = [tex]1.25 \times 10^5\;pa[/tex]
- Average kinetic energy = [tex]3.60 \times 10^{22}\;J[/tex]
Scientific data:
- Boltzmann constant (k) = [tex]1.38 \times 10^{-23}\;J/K[/tex]
- Ideal gas constant, R = 8.314 J/molK
To determine the number of moles of helium that are in the balloon, we we would use the ideal gas law equation;
[tex]n=\frac{PV}{RT}[/tex] ...equation 1.
Where;
- P is the pressure.
- V is the volume.
- n is the number of moles of substance.
- R is the ideal gas constant.
- T is the temperature.
First of all, we would determine the temperature of the spherical balloon by using this formula:
[tex]T=\frac{2}{3} \frac{K_E}{k} \\\\T = \frac{2}{3}\times \frac{3.60 \times 10^{-22}}{1.38 \times 10^{-23}} \\\\T = \frac{2}{3}\times 26.09\\\\T=17.39\;K[/tex]
Temperature, T = 17.39 K
Substituting the parameters into eqn. 1, we have;
[tex]n=\frac{1.25 \times 10^5\times 3.92 \times 10^{-3}}{8.314 \times 17.39}\\\\n=\frac{490}{144.58}[/tex]
n = 3.39 moles.
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