1. How much heat in kilojoules is needed to bring 2.00 kg of water from 27.7 to 82.6 ¡ãC (comparable to making four cups of coffee)?

2. Consider the reaction:

CH4(g) + 2O2(g) ¡ú CO2(g) + 2H2O(g)
Use data in table below

Compound S¡ã, J¡¤mol-1¡¤K-1
CH4(g) 186.2
O2(g) 205.0
CO2(g) 213.6
H2O(g) 188.7

a. calculate ¦¤S¡ã in J¡¤K-1.
-----?-------J¡¤K-1

b. From the standpoint of entropy only this reaction

i) is not spontaneous.

ii) occurs spontaneously.

I can't read some of the symbols.

1. To calculate the amount of heat needed to raise the temperature of water, we can use the formula:

Q = mcΔT

Where Q is the heat energy in Joules, m is the mass of water in kilograms, c is the specific heat capacity of water (4.18 J/g°C or 4180 J/kg°C), and ΔT is the change in temperature in Celsius.

First, convert the mass of water from grams to kilograms:

2.00 kg = 2000 g

Then calculate the change in temperature:

ΔT = 82.6°C - 27.7°C = 54.9°C

Now, we can calculate the heat energy using the formula:

Q = (2000 kg) x (4180 J/kg°C) x (54.9°C)

Q ≈ 458,556 Joules

To convert this value to kilojoules, divide by 1000:

Q ≈ 458.6 kilojoules

So, approximately 458.6 kilojoules of heat are needed to bring 2.00 kg of water from 27.7°C to 82.6°C.

2. To calculate the change in entropy (ΔS) for a reaction, we can use the formula:

ΔS = ΣnS°(products) - ΣmS°(reactants)

Where ΔS is the change in entropy, Σn is the stoichiometric coefficient of the products, S°(products) is the standard entropy of the products, Σm is the stoichiometric coefficient of the reactants, and S°(reactants) is the standard entropy of the reactants.

In this case, the reaction is:

CH4(g) + 2O2(g) → CO2(g) + 2H2O(g)

Using the given data from the table, we can find the standard entropy values:

S°(CH4) = 186.2 J/mol*K
S°(O2) = 205.0 J/mol*K
S°(CO2) = 213.6 J/mol*K
S°(H2O) = 188.7 J/mol*K

Applying the formula, we calculate:

ΔS = (1 x 213.6 J/mol*K) + (2 x 188.7 J/mol*K) - (1 x 186.2 J/mol*K) - (2 x 205.0 J/mol*K)

ΔS ≈ 410.4 J/mol*K

So, the change in entropy for the given reaction is approximately 410.4 J/mol*K.

b. From the standpoint of entropy only, to determine whether the reaction is spontaneous or not, we look at the sign of the change in entropy (ΔS).

i) If ΔS is positive, the reaction is spontaneous.
ii) If ΔS is negative, the reaction is not spontaneous.

In this case, ΔS is positive (410.4 J/mol*K), so the reaction occurs spontaneously from the standpoint of entropy only.