Use the equation for the synthesis of hydrogen to answer the following. 10 points.
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
To calculate the energy change (deltaH) when 5.00 g of carbon is consumed, you need to convert the mass of carbon to moles. The molar mass of carbon is 12.01 g/mol.
First, determine the number of moles of carbon:
molar mass of carbon = 12.01 g/mol
mass of carbon = 5.00 g
moles of carbon = mass of carbon / molar mass of carbon
= 5.00 g / 12.01 g/mol
≈ 0.416 moles
Now, use the given equation:
C (s) + H2O (l) -> CO (g) + H2 (g)
The coefficient in front of carbon (C) is 1, so the deltaH for the reaction is + 31.3 kcal/mol carbon.
deltaH = + 31.3 kcal/mol carbon
= + 31.3 kcal/mol * 0.416 moles
≈ + 13.0048 kcal
Therefore, the energy change (deltaH) when 5.00 g of carbon is consumed is approximately +13.0048 kcal.
To calculate the energy change (deltaH) when 2.50 moles of CO is produced, you can use the same equation and the given deltaH value.
First, determine the energy change for 1 mole of CO:
deltaH = + 31.3 kcal/mol carbon
Since the coefficient in front of CO is also 1, the deltaH for CO is the same as the deltaH for carbon:
deltaH (CO) = + 31.3 kcal/mol carbon
Now, calculate the deltaH for 2.50 moles of CO:
deltaH = deltaH (CO) * number of moles
= + 31.3 kcal/mol carbon * 2.50 mol
= + 78.25 kcal
Therefore, the energy change (deltaH) when 2.50 moles of CO is produced is +78.25 kcal.
To determine if the reaction is exothermic or endothermic, you can look at the sign of the deltaH value. If deltaH is positive, the reaction is endothermic. If deltaH is negative, the reaction is exothermic.
In the given equation, the deltaH value for the reaction is +31.3 kcal/mol carbon. Since the deltaH is positive, the reaction is endothermic.
To determine if the entropy (S) increases or decreases in the reaction, you can look at the sign of the deltaS value. If deltaS is positive, the entropy increases. If deltaS is negative, the entropy decreases.
In the given equation, the deltaS value is +32 cal/(mol•K). Since the deltaS value is positive, the entropy increases in this reaction.
To determine if the reaction is spontaneous or nonspontaneous at different temperatures, you can use the Gibbs free energy (deltaG) value. If deltaG is negative, the reaction is spontaneous. If deltaG is positive, the reaction is nonspontaneous.
To calculate the deltaG for this process at 300 K, you can use the Gibbs-Helmholtz equation:
deltaG = deltaH - T * deltaS
Given values:
deltaH = +31.3 kcal/mol carbon
deltaS = +32 cal/(mol•K)
T = 300 K
First, convert deltaH from kcal/mol to cal/mol:
deltaH = +31.3 kcal/mol carbon * 1000 cal/kcal
= +31,300 cal/mol carbon
Now, calculate deltaG:
deltaG = deltaH - T * deltaS
= +31,300 cal/mol carbon - 300 K * +32 cal/(mol•K)
= +31,300 cal/mol carbon - 9,600 cal/mol carbon
= +21,700 cal/mol carbon
Therefore, the deltaG for this process at 300 K is +21,700 cal/mol carbon.