Earnestness, n.
The state or quality of being earnest; intentness; anxiety. An honest earnestness in the young man's manner. W. Irving.
Shades of meaning
Fernald has no entry of its own for earnestness; he lists it under enthusiasm.
Where he writes about it:
Zeal is burning earnestness, always tending to vigorous action with all the devotion of enthusiasm, tho often without its hopefulness. — from enthusiasm