CO2 is available under following conditions: a pressure of 0.95 bar and 288 K temperature. Volume occupied by 100 kg of CO2 is?

Steps to Solve

1. Identify the Ideal Gas Law Formula

The ideal gas law is given by the formula: $$ PV = nRT $$ where:

• ( P ) = pressure (in Pa)
• ( V ) = volume (in m³)
• ( n ) = number of moles (mol)
• ( R ) = ideal gas constant ( \approx 8.314 , \text{J/(mol·K)} )
• ( T ) = temperature (in K)

2. Convert Parameters to Appropriate Units

First, convert the pressure from bar to pascals: $$ 1 , \text{bar} = 100000 , \text{Pa} $$ So, $$ P = 0.95 , \text{bar} = 0.95 \times 100000 , \text{Pa} = 95000 , \text{Pa} $$

3. Calculate the Number of Moles of CO2

The molar mass of CO2 (carbon dioxide) is approximately ( 44.01 , \text{g/mol} ).

First, convert the mass from kg to grams: $$ 100 , \text{kg} = 100000 , \text{g} $$

Now calculate the number of moles: $$ n = \frac{\text{mass}}{\text{molar mass}} = \frac{100000 , \text{g}}{44.01 , \text{g/mol}} \approx 2272.15 , \text{mol} $$

4. Substitute Values in Ideal Gas Law

Now we can substitute the values into the ideal gas law to find the volume ( V ): $$ V = \frac{nRT}{P} $$

Substituting the values: $$ R = 8.314 , \text{J/(mol·K)} = 8.314 , \text{m}^3 , \text{Pa/(mol·K)} $$

Calculating ( V ): $$ V = \frac{(2272.15 , \text{mol}) \times (8.314 , \text{m}^3 , \text{Pa/(mol·K)}) \times (288 , K)}{95000 , \text{Pa}} $$

5. Calculate the Final Volume

Calculating the numerator: $$ 2272.15 \times 8.314 \times 288 \approx 5,661,675.3 , \text{m}^3 , \text{Pa} $$

Now divide by the pressure: $$ V \approx \frac{5661675.3}{95000} \approx 59.18 , \text{m}^3 $$

6. Select the Closest Answer

Reviewing the provided options, we look for the closest match. The given options are:

• 15.90 m³
• 25.74 m³
• 68.13 m³
• 56.57 m³

The closest value is 56.57 m³.