Question

To test the effectiveness of a gunpowder mixture, 1 gram was exploded under controlled STP conditions, and the reaction chamber was found to expand to 310 cm3. What volume would these gases occupy at the temperature produced by an uncontrolled explosion (2,200°C) and 2.1 atmospheres of pressure? 5,900 cm3 1,300 cm3 7.7 x 104 cm3 1,000 cm3

Answer 1

1300 cm 3

Step-by-step explanation:

Answer 2

The volume of the gas at given temperature is
`1300 cm^3`

Step-by-step explanation:

`P_1` = initial pressure of gas = 1 atm

`T_1` = initial temperature of gas =
`0^oC=273.15 K`

`V_1` = initial volume of gas =
`310 cm^3 = 310 mL = 0.310 L`

(
`1 cm^3= 1mL` , 1 mL = 0.001 L)

`P_1V_1=nRT_1`..[1]

`P_2` = final pressure of gas = 2.1 atm

`T_2` = final temperature of gas =
`2,200^oC=273+2200 K=2473.15 K`

`V_2` = final volume of gas = ?

`P_2V_2=nRT_2`..[2]

By dividing [1] and [2] we get combined gas equation :,

`(P_1V_1)/(T_1)=(P_2V_2)/(T_2)`

`V_2=(P_1V_1* T_2)/(T_1* P_2)`

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

`V_2=(1 atm* 0.310 L* 2473.15 K)/(273.15 K* 2.1 atm)`

`V_2=1.3 L=1300 mL= 1300 cm^3`

The volume of the gas at given temperature is
`1300 cm^3`