How many of the following have standard heat of formation is zero.
(i) `Br_(2(l))` (ii) `CO_(2(g))` (iii) `C_("graphite")` (iv) `Cl_(2(l))` (v) `Cl_(2(g))`
(vi) `F_(2(g))` (vii) `F_((g))` (viii) `l_(2(g))` (ix) `S_(("monoclinic"))` (x) `N_(2(g))`
(xi) `P_(("Black"))` (xii)`P_((red))` (xiii) `CH_(4)`

Explanation

To determine how many of the given substances have a standard heat of formation of zero, we need to identify which of these substances exist in their most stable form at standard conditions (1 atm pressure and 25°C). The standard heat of formation for elements in their standard state is defined as zero.

### Step-by-Step Solution:

1. **Identify the substances:**
The substances given are:
- (i) \( \text{Br}_{2(l)} \)
- (ii) \( \text{CO}_{2(g)} \)
- (iii) \( \text{C}_{\text{(graphite)}} \)
- (iv) \( \text{Cl}_{2(l)} \)
- (v) \( \text{Cl}_{2(g)} \)
- (vi) \( \text{F}_{2(g)} \)
- (vii) \( \text{F}_{(g)} \)
- (viii) \( \text{I}_{2(g)} \)
- (ix) \( \text{S}_{\text{(monoclinic)}} \)
- (x) \( \text{N}_{2(g)} \)
- (xi) \( \text{P}_{\text{(Black)}} \)
- (xii) \( \text{P}_{(red)} \)
- (xiii) \( \text{CH}_{4} \)

2. **Determine the standard states:**
- \( \text{Br}_{2(l)} \): Bromine in liquid state is a stable form. **Heat of formation = 0**
- \( \text{CO}_{2(g)} \): Carbon dioxide is a compound, not an element in its standard state. **Heat of formation ≠ 0**
- \( \text{C}_{\text{(graphite)}} \): Graphite is the stable form of carbon. **Heat of formation = 0**
- \( \text{Cl}_{2(l)} \): Chlorine in liquid state is not the standard state; it is gaseous at standard conditions. **Heat of formation ≠ 0**
- \( \text{Cl}_{2(g)} \): Chlorine gas is the stable form of chlorine. **Heat of formation = 0**
- \( \text{F}_{2(g)} \): Fluorine gas is the stable form of fluorine. **Heat of formation = 0**
- \( \text{F}_{(g)} \): A single fluorine atom is not stable; it does not exist freely. **Heat of formation ≠ 0**
- \( \text{I}_{2(g)} \): Iodine is solid at standard conditions, not gas. **Heat of formation ≠ 0**
- \( \text{S}_{\text{(monoclinic)}} \): Monoclinic sulfur is a stable form. **Heat of formation = 0**
- \( \text{N}_{2(g)} \): Nitrogen gas is the stable form of nitrogen. **Heat of formation = 0**
- \( \text{P}_{\text{(Black)}} \): Black phosphorus is a stable form. **Heat of formation = 0**
- \( \text{P}_{(red)} \): Red phosphorus is also a stable form. **Heat of formation = 0**
- \( \text{CH}_{4} \): Methane is a compound, not an element in its standard state. **Heat of formation ≠ 0**

3. **Count the substances with zero heat of formation:**
The substances that have a standard heat of formation of zero are:
- \( \text{Br}_{2(l)} \)
- \( \text{C}_{\text{(graphite)}} \)
- \( \text{Cl}_{2(g)} \)
- \( \text{F}_{2(g)} \)
- \( \text{S}_{\text{(monoclinic)}} \)
- \( \text{N}_{2(g)} \)
- \( \text{P}_{\text{(Black)}} \)
- \( \text{P}_{(red)} \)

This gives us a total of **8 substances**.

### Final Answer:
**8 substances have a standard heat of formation of zero.**