H2S+KMnO4+H2SO4---K2SO4+S8+MnSO4+H2O
If you can't think of any better way to balance one of these beasts you can always do this:
$\displaystyle aH_2S + bKMnO_4 + cH_2SO_4 \to dK_2SO_4 + eS_8 + fMnSO_4 + gH_2O$
where the a, ..., g are your balancing coefficients.
Now work through each element on each side of the reaction:
For H:
2a + 2c = 2g
For S:
a + c = d + 8e + f
etc.
Now solve the system of equations:
2a + 2c = 2g
a + c = d + 8e + f
b = 2d
b = f
4b + 4c = 4d + 4f + g
f = b, so:
2a + 2c = 2g
a + c = d + 8e + b
b = 2d
4c = 4d + g
From the bottom: g = 4c - 4d so:
2a = 6c - 8d
a + c = d + 8e + b
b = 2d
b = 2d, so:
2a = 6c - 8d
a + c = 3d + 8e
From the bottom, c = 3d + 8e - a so:
8a = 10d + 48e
4a = 5d + 24e
e = (1/24)(4a - 5d) = a/6 - 5d/24
Now we need to pick some convenient values for a and d:
I'll try a = 36, d = 24 (These are the smallest values that make e an integer and positive):
e = 1, c = 44, b = 48, g = 80, f = 48
So:
$\displaystyle 36H_2S + 48KMnO_4 + 44H_2SO_4 \to 24K_2SO_4 + S_8 + 48MnSO_4 + 80H_2O$
-Dan