Final answer:
To find the number of molecules in the gas sample, convert the pressure to atmospheres and the temperature to Kelvin, then use the ideal gas law to calculate moles, and finally multiply by Avogadro's number to get the number of molecules.
Step-by-step explanation:
To calculate the number of molecules in a gas sample given its volume, temperature, and pressure, you can use the ideal gas law in combination with Avogadro's number. The ideal gas law is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. Since the pressure is given in torr, it must first be converted to atmospheres (1 atm = 760 torr). The temperature must be converted from Celsius to Kelvin (K = °C + 273.15).
The number of moles (n) can then be calculated using the ideal gas law. Once you have the moles, you can find the number of molecules by multiplying the number of moles by Avogadro's number (6.022 x 1023 molecules/mol).
First, convert the given pressure and temperature: P (in atm) = 624 torr / 760 torr/atm; T (in K) = 185 °C + 273.15.
Once you have P in atm and T in K, plug these values into the ideal gas constant with R = 0.0821 L·atm/mol·K:
n = PV / (RT)
Then, calculate the number of molecules: Number of molecules = n × Avogadro's number