Answer
There are $~4.83\times 10^{21}~$ gas molecules in the chamber.
Work Step by Step
We can find the number of moles $n$:
$Q = c_v~n~\Delta T$
$n = \frac{Q}{c_v~\Delta T}$
$n = \frac{Q}{1.5~R~\Delta T}$
$n = \frac{10.0~J}{(1.5)(8.314~J/mol~K)(100~K)}$
$n = 0.00802~mol$
We can find the number of molecules:
$N = (0.00802~mol)(6.022\times 10^{23}) = 4.83\times 10^{21}$
There are $~4.83\times 10^{21}~$ gas molecules in the chamber.
