Carbon disulfide reacts with oxygen to form carbon dioxide and sulfur dioxide.

#CS_2 + O_2 -> CO_2 + SO_2#

Start by finding the number of moles of the carbon dioxide produced.

#37.8 \ "g" \ CS_2 xx ( 1\ "mol."\ CS_2)/(76.1407 \ "g" \ CS_2)xx ("1 mol."\ CO_2)/( 1 \ "mol."\ CS_2)#

#37.8 \cancel ( "g" \ CS_2) xx ( color(red) cancel( 1\ "mol."\ CS_2))/(76.1407 \cancel( "g" \ CS_2))xx ("1 mol."\ CO_2)/(color (red) cancel( 1\ "mol."\ CS_2))#

#0.496 \ mol. \ CO_2#

Now use the ideal gas equation to figure out the the volume of the #CO_2# produced.

# P*V= n*R*T#

Where

#P" "# is the pressure expressed in atm.

#V" "# is the volume expressed in L.

#n" " # is the number of moles.

#R" "# is the universal gas constant, it has a value of #0.0821\ L* atm. mol^-1*K^-1#

#T" " #is the Kelvin temperature.

Now rearrange the ideal gas equation and solve for V.

# V= (n*R*T)/P#

# V= (0.496\ molxx0.0821\ L*atm*mol^-1*K^-1 xx 302.00 \ K)/ (1.02\ atm)#

#V= (0.496\cancel( mol)xx0.0821\ L*cancel(atm)*cancel(mol^-1)*cancel(K^-1)xx 302.00 \cancel(K))/ (1.02\ cancel(atm))#

#V= 12.1 \ L#