Use the equation for the synthesis of hydrogen to answer the following.
C (s) + H2O (l) -> CO (g) + H2 (g)
deltaH = + 31.3 kcal/mol carbon
deltaS = +32 cal/(mol•K)
Calculate the energy change (deltaH) when 5.00 g of carbon is consumed.
Calculate the energy change (deltaH) when 2.50 moles of CO is produced.
This reaction is exothermic/endothermic.
The entropy increases/decreases in this reaction
At low temperatures this reaction is spontaneous/nonspontaneous
At high temperatures this reaction is spontaneous/nonspontaneous
Calculate the deltaG for this process at 300. K
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a.
31.3 kcal/mol x (5.00/12) = ? kcal
b.
31.3 kcal/mol x 2.5 mol CO = ? kcal
c.
A + dH means endothermic.
A + dS means entropy is increasing.
d.
Do e first. Then set dG to zero, substitute for dH and dS and solve for T. Remember dH is in kcal/mol while dS is in cal/mol
e.
dG = dH - TdS
To calculate the energy change (deltaH) when 5.00 g of carbon is consumed, we need to convert the mass of carbon to moles and then use the given deltaH value.
Step 1: Convert mass of carbon to moles
Given mass of carbon: 5.00 g
Molar mass of carbon (C): 12.01 g/mol
moles of carbon = mass of carbon / molar mass of carbon
moles of carbon = 5.00 g / 12.01 g/mol
Step 2: Calculate the energy change (deltaH)
deltaH = deltaH per mole of carbon * moles of carbon
deltaH = +31.3 kcal/mol carbon * moles of carbon
Substitute the value of moles of carbon from Step 1 into the equation:
deltaH = +31.3 kcal/mol carbon * (5.00 g / 12.01 g/mol)
Calculate the value to find the energy change (deltaH) when 5.00 g of carbon is consumed using the given equation.
To calculate the energy change (deltaH) when 2.50 moles of CO is produced, we can use the given deltaH value directly since it is given per mole of carbon:
deltaH = +31.3 kcal/mol carbon
Since 1 mole of CO is produced for every mole of carbon consumed, the energy change (deltaH) for producing 2.50 moles of CO would be the same as the energy change for consuming 2.50 moles of carbon. Therefore, the value of deltaH would be:
deltaH = +31.3 kcal/mol carbon
Now, let's answer the remaining questions:
1. This reaction is exothermic because the given deltaH value is positive (+31.3 kcal/mol carbon).
2. The entropy increases in this reaction because the given deltaS value is positive (+32 cal/(mol•K)).
3. At low temperatures, this reaction is nonspontaneous because the deltaG value is positive at low temperatures (deltaG = deltaH - T * deltaS, where T is the temperature in Kelvin).
4. At high temperatures, this reaction is spontaneous because the deltaG value is negative at high temperatures (deltaG = deltaH - T * deltaS, where T is the temperature in Kelvin).
5. To calculate the deltaG for this process at 300 K, we can use the formula:
deltaG = deltaH - T * deltaS
Substitute the given values into the equation:
deltaG = +31.3 kcal/mol carbon - 300 K * (+32 cal/(mol•K))
Convert calories to kilocalories and substitute the appropriate conversion factor:
deltaG = +31.3 kcal/mol carbon - 300 K * (+0.032 kcal/(mol•K))
Calculate the value to find the deltaG for this process at 300 K using the given equation.