A flash bulb used for taking photograph in poor light contains `30 mL` of `O_(2)` at `780 mm` pressure at `27^(@)C`. Suppose that metal wire flashed in the bulb is pure aluminium `(Al)` and it is oxidised to `Al_(2) O_(3)` in the process of flashing, calculate the minimun weight of `Al` wire that is to be used for maximum efficiency.

Options

A. `0.045 g`
B. `0.05 g`
C. `0.04 g`
D. `0.055 g`

Answer

A

Explanation

`Al` is oxiddised to `Al_(2) O_(3)` as follows
`4 Al + 3 O_(2) rarr 2 Al_(2) O_(3)`
First, calculate the moles `(n)` of `O_(2)`
Use `Pv = nRT`
`implies n = (PV)/(RT) = ((780//760)(30//1000))/(0.082 xx 300) = 1.25 xx 10^(-3)`
From stoichiometry of reaction:
3 mol of `O_(2) -= 4 mol of Al`
`1.25 xx 10^(-3) mol of O_(2) -= (4)/(3) (1.25 xx 10^(-3)) mol of Al`
Weight of `Al = (4)/(3) (1.25 xx 10^(-3)) xx 27 = 0.045 g`