To solve this we need to use the ideal gas law equation PV=nRT. We are asked to calculate the volume at STP which means standard temperature and pressure. That means 1 atm of pressure and 25 *C. But we are given the initial values for a temperature of 37 *C. So we need to use the information given to solve for the number of moles (n) of the gas, and then use this number to solve for the volume at STP. Setting up to solve for n:
Since the R value we use is 0.0821 L atm/mol K, we need to get the pressure in terms of atm and the temperature in terms of K. 1 atm is equal to 760 mmHg, so we will use that conversion factor.
669 mmHg * (1 atm/760 mmHg) = 0.88 atm
To convert from Celcius to Kelvin, simply add 273 to the number. So 37 Celcius is equal to 37 + 273 = 310 K.
n = PV/RT = [(0.88 atm)(7 L)]/[(0.0821 Latm/molK)(310 K)] = 0.242 moles of gas
So now we can substitute this number of moles of gas back into the gas law equation to solve for the volume at 1 atm and 273 K.
v=(nRT)/P = [(0.242 mol)(0.0821 Latm/molK)(273 K)]/1 atm = 5.42 L
So the answer is 5.42 Liters.