A 10.5 gram sample of carbon dioxide gas has a volume of 986 milliliters at a pressure of 3.72 atm. The temperature of the gas sample is
°C.
To find the temperature of the gas sample in Celsius, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure in atm (3.72 atm)
V = volume in liters (986 ml = 0.986 L)
n = moles of gas (we can find this from the mass of the gas)
R = ideal gas constant (0.0821 L*atm/mol*K)
First, we need to find the moles of gas using the mass given:
10.5 g CO2 * (1 mol CO2 / 44.01 g CO2) = 0.238 mol CO2
Now we can plug in the values into the ideal gas law equation:
(3.72 atm) * (0.986 L) = (0.238 mol) * (0.0821 L*atm/mol*K) * T
T = (3.65592 atm*L) / (0.019558 mol)
T = 186.6 K
To convert from Kelvin to Celsius, subtract 273.15:
186.6 K - 273.15 = -86.55 °C
Therefore, the temperature of the gas sample is -86.55 °C.