This question will primarily focus on using stoichiometric molar ratio's to find a solution.
The balanced reaction C6H12O6 + 6O2 = 6CO2 + 6H2O provides such molar ratio's in the stoichiometric coefficients of each chemical species, which we will see as we solve this problem.
To begin, the problem states that during cellular respiration, 180g of glucose (C6H12O6) are consumed in the process. Being that the stoichiometric coefficients in our balanced reaction equation above describe molar quantities, we will need to convert our mass of glucose into moles of glucose. Doing so is relatively straight forward. All we need to do is divide the mass of glucose (in grams) by the molar mass of glucose (in grams/mole).
The molar mass of glucose (C6H12O6) is approximately 180.156 g/mole.
Moles of Glucose = (Mass of Glucose) / (Molar Mass of Glucose)
Moles of Glucose = (180g) / (180.156g) = 0.999134 moles of Glucose
Now that we know the number of moles of glucose contained in the 180g of glucose consumed during our reaction, we can use the stoichiometric ratios of the balanced reaction to find the number of moles of oxygen consumed in the process.
On the reactant side of the reaction, the stoichiometric coefficient of Glucose (C6H12O6) is 1, whereas the stoichiometric coefficient of the diatomic gaseous oxygen (O2) is 6.
This means that for every 1 mole of glucose consumed in the reaction, 6 moles of oxygen are consumed in order to produce the products listed in the reaction.
So, in order for our 0.999134 moles of glucose to be fully consumed, 6 times that number of moles of oxygen must also be consumed.
Moles of Oxygen Consumed = 6*(Moles of Glucose Consumed)
Moles of Oxygen Consumed = 6*(0.999134 moles) = 5.9948 moles of oxygen consumed.
Now that we know the number of moles of oxygen consumed, we can solve for the mass of oxygen consumed using the molar mass of oxygen gas, similar to how we converted our initial mass of glucose into moles of glucose.
The molar mass of oxygen gas (O2) is 2*16 = 32 g/mol. This is because there are two oxygen atoms in each molecule of oxygen gas.
To find the mass of oxygen consumed, all that is required is to multiply the number of moles of oxygen gas by the molar mass of oxygen gas.
Mass of oxygen consumed (g) = Moles of oxygen consumed * Molar mass of oxygen gas
Mass of oxygen consumed (g) = (5.9948 moles O2) * (32 g/mole) = 191.834 g of oxygen gas.
Thus, we now know that 191.834 grams of diatomic oxygen gas (O2) were consumed during this cellular respiration process in order to fully react all 180 grams of glucose initially present in the system.
I hope this helped!