Answer:
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Explanation:
Stoichiometry is very easy to master if you understand the ‘mole concept’ and how it is used to define and describe chemical process mathematically. A ‘mole’ – in chemistry – is the mass of substance containing one Avogadro’s Number of particles. That is, N₀ = 6.023 x 10²³ particles / mole. When working with chemical reactions and equations data should be first converted to moles using the following conversations:
1 mole = 1 formula weight = 6.023 x 10²³ particles = 22.4 liters at STP(0⁰, 1atm).
In this problem you are given the equation Na + H₂O => NaOH + H₂. ‘Reading the equation’ there is 1 mole of Na, 1 mole of water, 1 mole of NaOH and 1 mole of H₂. In another example 3H₂ + N₂ => 2NH₃ there are 3 moles of H₂, 1 mole of N₂ and 2 moles of NH₃. The mole values can be multiples or fractions but if one mole value increases all the remaining mole values increase or decrease proportionally. For example:
Using the equation Na + H₂O => NaOH + H₂, one could apply a 2 before the Na but all the following formulas would need be increased by a factor of 2. If one applies ½ to the Na then all the following formulas would need be cut in half also and the reaction stoichiometry would still be valid. The fact that the equation is written with coefficients of 1 is that it is in the smallest whole number ratio of coefficients. This then implies the reaction formula is in ‘standard form’. This also implies the equation conditions are at 0⁰C & 1atm pressure and 1 mole of any gas phase substance occupies 22.4 Liters volume. Such is the significance of converting given data to moles as all other substance mass (in moles) are proportional.
For your 1st problem, 1.76 x 10²⁴ formula units of Na will react with water (usually read as an excess) to produce (?) grams of H₂.
1st write the equation followed by listing the givens below the respective formulas… That is…
Na + H₂O => NaOH + H₂,
Given: 1.76 x 10²⁴ atoms excess --------- ? grams
Convert atoms Na to moles = 1.76 x 10²⁴atoms/6.023 x 10²³atoms/mole
=2.922moles Na produces=>2.922moles H₂(because moles Na=moles H₂).
Convert moles to grams =>2.922moles H₂ x 2.000 grams H₂/mole H₂
=5.8443 grams H₂
2nd problem, 3.5 moles Na will react with H₂O (in excess) to produce (?) moles of NaOH.
Again write equation and assign values to each formula unit in the equation.
Na + H₂O => NaOH + H₂,
Given: 3.5moles excess ? grams ----
Since coefficients of balanced std equation are equal then moles Na equals moles of NaOH, that is, 3.5 moles Na produces => 3.5 moles NaOH
Convert moles NaOH to grams => 3.5 moles NaOH x 40 g NaOH/mole NaOH = 140 grams NaOH
3rd problem, 2.75 x 10²⁵ molecules H₂O will react with (?) atoms of Na.
Same procedure, convert to moles, solve problem by ratios then convert to needed dimension at end of problem.
Na + H₂O => NaOH + H₂
Given: ? atoms 2.75 x 10²⁵ molecules H₂O => NaOH + H₂
Convert to moles => 2.75 x 10²⁵ molecules H₂O / 6.023 x 10²³ molecules H₂O/mole H₂O = 45.658 moles H₂O => 45.658 moles Na (equal coefficients)
Convert moles Na to atoms Na => 45.658 moles Na x 6.023 x 10²³atoms Na/mole Na = 2.75 x 10²⁵ atoms Na.
Note => Problem 3 could have been solved by inspection b/c coefficients are equal, however, always go through a process that you can justify and defend even if it does take longer. Never assume anything. Depend on what you know, not what you 'think' you know.
Master the mole concept and you master a lot of chemistry! Good luck.
π(9). When you solve it you end up with a radius of 2 in which you multiply by 1.2 which gives you the radius of the new cylinder which is 2.4. With the new radius you simply find the volume of the bigger cylinder which is 51.94π
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