To solve this problem, we need to use the ideal gas law, which relates the pressure, volume, and temperature of a gas:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.
We can rearrange this equation to solve for the number of moles:
n = PV / RT
First, we need to convert the given values to SI units. The pressure is given in torr, which can be converted to Pascals (Pa) using the conversion factor:
1 torr = 133.322 Pa
So, P = 736 torr = 98,365 Pa
The volume is given in milliliters (mL), which can be converted to cubic meters (m^3) using the conversion factor:
1 mL = 1 x 10^-6 m^3
So, V = 20 mL = 2 x 10^-5 m^3
The temperature is given in degrees Celsius (°C), which needs to be converted to Kelvin (K):
T (K) = T (°C) + 273.15
So, T = 25°C + 273.15 = 298.15 K
The gas constant R is a constant value:
R = 8.314 J/(mol·K)
Now we can plug in these values to find the number of moles of gas:
n = PV / RT
= (98,365 Pa) x (2 x 10^-5 m^3) / (8.314 J/(mol·K) x 298.15 K)
= 0.00395 mol
Therefore, there are 0.00395 moles of gas in the container.