you have 5.1 x 10^22 molecules of an ideal gas. you measure the temperature of the gas to be 8 °c and the…

Explanation:

Step1: Convert temperature to Kelvin

$T=(8 + 273.15)\text{ K}=281.15\text{ K}$

Step2: Convert volume to $m^3$

$V = 4102\times10^{- 6}\text{ m}^3=4.102\times10^{-3}\text{ m}^3$

Step3: Calculate number of moles

$n=\frac{N}{N_A}$, where $N = 5.1\times10^{22}$ and $N_A=6.022\times10^{23}\text{ mol}^{-1}$ $n=\frac{5.1\times10^{22}}{6.022\times10^{23}}\text{ mol}\approx0.0847\text{ mol}$

Step4: Use ideal - gas law $PV = nRT$ to find pressure

$P=\frac{nRT}{V}$ $P=\frac{0.0847\text{ mol}\times8.314\text{ J}\text{ mol}^{-1}\text{ K}^{-1}\times281.15\text{ K}}{4.102\times10^{-3}\text{ m}^3}$ $P=\frac{0.0847\times8.314\times281.15}{4.102\times10^{-3}}\text{ Pa}$ $P\approx4.83\times10^{4}\text{ Pa}$

Answer:

$4.83\times10^{4}\text{ Pa}$