Question

Calculate the number of moles of an ideal gas if it occupies 0.01 m3 under 125,000 Pa at a temperature of 357 K.

Answer 1

Answer : The correct option is, (A) 0.42 moles

Explanation :

Using ideal gas equation:

$PV=nRT$

where,

P = pressure of gas = 125000 Pa = 125 kPa

conversion used : (1 kPa = 1000 Pa)

V = volume of gas = $0.01m^3=10L$

conversion used : $(1m^3=1000L)$

T = temperature of gas = 357 K

n = number of moles of gaseous mixture = ?

R = gas constant = 8.314 kPa.L/mol.K

Now put all the given values in the ideal gas equation, we get:

$(125kPa)\times (10L)=n\times (8.314kPa.L/mol.K)\times (357K)$

$n=0.42mole$

Therefore, the number of moles of an ideal gas is 0.42 mole.

Answer 2

The correct answer is A. 0.42 moles.

Further Explanation

The Ideal Gas Equation states the relationship among the pressure, temperature, volume, and number of moles of a gas.

The Ideal Gas Equation is:  

where:  

P - pressure (in Pa)  

V - volume (in m³)  

n - amount of gas (in moles)  

R - universal gas constant  (8.314 Pa·m³/mol·K)

T - temperature (in K)  

In the problem, we are given the values:  

P = 125,000 Pa (3 significant figures)

V =0.01 m³  (1 significant figure)

n = ?

T = 357 K (3 significant figures)  

Solving for n using the Ideal Gas Equation:  

$PV = nRT$$n = \frac{PV}{RT}\\n = \frac{125,000 \ Pa \times 0.01 \ m^3}{8.314 \frac{Pa-m^3}{mol-K} \times 357 \ K}\\n = \frac{1250 \ Pa-m^3}{2968 \frac{Pa-m^3}{mol}}\\\\\boxed {n = 0.42116 \ mol}$

The least number of significant figures is 1, therefore, the final answer must have only 1 significant figure:

$\boxed {\boxed {n = 0.4 \ mol}}$

Since this is not available, the closest answer is option A. 0.42 moles.

Learn More  

1. Learn more about Boyle's Law brainly.com/question/1437490  

2. Learn more about Charles' Law brainly.com/question/1421697  

3. Learn more about Gay-Lussac's Law brainly.com/question/6534668

Keywords: Ideal Gas Law, Volume, Pressure