We write DE = q+w, where DE is the internal energy change and q and w are heat and work, respectively.
(b)Under what conditions will the quantities q and w be negative numbers?
q is negative when heat flows from the system to the surroundings, and w is negative when the system does work on the surroundings.
As an aside: In applying the first law, do we need to measure the internal energy of a system? Explain.
The absolute internal energy of a system cannot be measured, at least in any practical sense. The internal energy encompasses the kinetic energy of all moving particles in the system, including subatomic particles, as well as the electrostatic potential energies between all these particles. We can measure the change in internal energy (DE) as the result of a chemical or physical change, but we cannot determine the absolute internal energy of either the initial or the final state. The first law allows us to calculate the change in internal energy during a transformation by calculating the heat and work exchanged between the system and its surroundings.
 
        
             
        
        
        
The <u>Mole</u> is the SI unit that expresses the amount of substance.
Mole is defined as - The mole is the amount of substance containing the same number of entities as there are in the 12 grams of Carbon - 12. 
Mole is denoted by using symbol mol. 
       Mole = 6.022 x 10²³ elementary entities.
These number of elementary entities in 1 mole is equal to or called as an Avogadro's number.  Mole is equal to 6.022 x 10²³ because this number of entity is same as in exactly 12 g of carbon-12.
It is a very important SI unit of measured which is used by the chemists. Moles are used in measuring in small or tiny things such as atoms, molecules and the other tiny particles. 
To learn more about the mole concept, 
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Agar is used to assist establish an anaerobic environment that promotes nitrate reduction.
Nitrate Reduction test:
- The nitrate in the broth is converted to nitrite by organisms that can produce the nitrate reductase enzyme, which can then be further converted to nitric oxide, nitrous oxide, or nitrogen.
 -  Anaerobic respiration and denitrification are two processes that can convert nitrate to a variety of compounds. 
 - While denitrification only reduces nitrate to molecular nitrogen, anaerobic respiration employs nitrate as the bacterium's final electron acceptor, reducing it to a range of chemicals.
 - The nitrate reduction test is based on the detection of nitrite and its capacity to produce a red precipitate (prontosil), which is a water-soluble azo dye, when it combines with sulfanilic acid to create a complex (nitrite-sulfanilic acid).
 
Learn more about the Nitrate reduction test with the help of the given link:
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Answer:
2.12×10²³ atoms.
Explanation:
From Avogadro's hypothesis, we understood that 1 mole of any substance contains 6.02×10²³ atoms. This simply means that 1 mole of zirconium also 6.02×10²³ atoms.
Thus, we can obtain the number of atoms present in 0.3521 mole of zirconium as follow:
1 mole of zirconium also 6.02×10²³ atoms.
Therefore, 0.3521 mole of zirconium will contain = 0.3521 × 6.02×10²³ = 2.12×10²³ atoms.
Therefore, 0.3521 mole of zirconium contains 2.12×10²³ atoms.
 
        
             
        
        
        
 I think it 2.25 or somethingg