Since the sample inside the syringe is a gas, we assume that it is an ideal gas that is we use the expression PV = nRT. We can easily calculate the pressure as follows:
n = m /MM = 0.10 / 28 = 0.0036 mol
P = nRT / V = 0.0036(0.08206)(273.15) / 0.010
P = 8 atm
