Question

Suppose you have 0.100 m3 of co2, at pressure of 2.00 atm, and a temperature of 30.0◦c. how many grams of co2 do you have? express your answer in grams.

Answer 1

Use Ideal Gas equation since values are given in Pressure (P), Volume (V), Temperature (T).                                  P V = n R T ; n= PV / RT
To choose the value of R ( gas constant), check out the units of other values in the equation. They are in atm,m³, kelvin, and mole.  So, its value is 8.205 m³ atm K⁻¹ mol⁻¹

P= 2.00 atmV= 0.100 m³R= 8.205 m³ atm K⁻¹ mol⁻¹T= (30+ 273) K ( recall Kelvin = Celcius + 273; K= °C + 273)
Substitute values into equation of  n= PV / RT 

n=2.00 atm * 0.100 m³ / 8.205 m³ atm K⁻¹ mol⁻¹ * 303 K = 8.04 * 10⁻⁵ mole

Mole of CO₂ is  8.04 * 10⁻⁵. Its molar mass is 44 g/mol.

To find out its mass use mole= mass / Molar mass ; n= m/ M; m= n M

m= (8.04 * 10⁻⁵ mol) (44 g/mol) = 0. 035 g

The answer is 0.035 g

Answer 2

Answer: 353.936 grams of $CO_2$ will be there.

Explanation: Using Ideal gas equation, which is:

$PV=nRT$

Given:

P = 2 atm

$V=0.1m^3=100L$   (Conversion Factor: $1m^3=1000L$ )

$T=30^oC=(273+30)K=303K$   (Conversion factor = 0°C = 273 K)

$R=0.082057\text{ L atm }mol^{-1}K^{-1}$  (Gas Constant)

Putting all the values in above equation, we calculate the number of moles.

$2atm\times 100L=n(0.082057\text{ L atm }mol^{-1}K^{-1})(303K)$

n = 8.044 moles

Now, to calculate the grams of $CO_2$, we use the formula:

$Moles=\frac{\text{Given mass}}{\text{Molar mass}}$

Molar mass of $CO_2=44g/mol$

Putting the values in above equation, we get

$8.044mol=\frac{\text{Given mass}}{44g/mol}$

Mass of $CO_2$ = 353.936 g